Embed Size (px)
Citation preview
Linear Equations Example 1
Find solutions to the equation:We can start by Subtracting 4 from each side
3x2 = 9
Next, Multiply by 2 on each side3x = 18
Finally, we will Divide by 3 on each side to getThe solution to the equation is x = 6
Linear Equations Example 1
Find solutions to the equation:3x2 + 4 = 13
We can start by Subtracting 4 from each side3x2 = 9
Next, Multiply by 2 on each side3x = 18
Finally, we will Divide by 3 on each side to getThe solution to the equation is x = 6
Linear Equations Example 1
Find solutions to the equation:3x2 + 4 = 13
We can start by Subtracting 4 from each side3x2 = 9
Next, Multiply by 2 on each side3x = 18
Finally, we will Divide by 3 on each side to getThe solution to the equation is x = 6
Linear Equations Example 1
Find solutions to the equation:3x2 + 4 = 13
We can start by Subtracting 4 from each side3x2 = 9
Next, Multiply by 2 on each side3x = 18
Finally, we will Divide by 3 on each side to getThe solution to the equation is x = 6
Linear Equations Example 1
Find solutions to the equation:3x2 +4 = 13
We can start by Subtracting 4 from each side3x2 = 9
Next, Multiply by 2 on each side3x = 18
Finally, we will Divide by 3 on each side to getThe solution to the equation is x = 6
Linear Equations Example 1
Find solutions to the equation:3x2 +4 = 13 Address fraction first
We can start by Subtracting 4 from each side
3x2 = 9
Next, Multiply by 2 on each side3x = 18
Finally, we will Divide by 3 on each side to getThe solution to the equation is x = 6
Linear Equations Example 1
Find solutions to the equation:3x2 +4 = 13 Address fraction first
We can start by Subtracting 4 from each side3x2 +4 − 4 = 13−4
3x2 = 9
Next, Multiply by 2 on each side3x = 18
Finally, we will Divide by 3 on each side to getThe solution to the equation is x = 6
Linear Equations Example 1
Find solutions to the equation:3x2 +4 = 13 Address fraction first
We can start by Subtracting 4 from each side3x2 = 3x
2 ����+4 − 4 = 13−4
3x2 = 9
Next, Multiply by 2 on each side3x = 18
Finally, we will Divide by 3 on each side to getThe solution to the equation is x = 6
Linear Equations Example 1
Find solutions to the equation:3x2 +4 = 13 Address fraction first
We can start by Subtracting 4 from each side3x2 = 3x
2 ����+4 − 4 = 13−4 = 9
3x2 = 9
Next, Multiply by 2 on each side3x = 18
Finally, we will Divide by 3 on each side to getThe solution to the equation is x = 6
Linear Equations Example 1
Find solutions to the equation:3x2 +4 = 13 Address fraction first
We can start by Subtracting 4 from each side3x2 = 3x
2 ����+4 − 4 = 13−4 = 93x2 = 9
Next, Multiply by 2 on each side3x = 18
Finally, we will Divide by 3 on each side to getThe solution to the equation is x = 6
Linear Equations Example 1
Find solutions to the equation:3x2 +4 = 13 Address fraction first
We can start by Subtracting 4 from each side3x2 = 3x
2 ����+4 − 4 = 13−4 = 93x2 = 9
Next, Multiply by 2 on each side
3x = 18Finally, we will Divide by 3 on each side to getThe solution to the equation is x = 6
Linear Equations Example 1
Find solutions to the equation:3x2 +4 = 13 Address fraction first
We can start by Subtracting 4 from each side3x2 = 3x
2 ����+4 − 4 = 13−4 = 93x2 = 9
Next, Multiply by 2 on each side2 · 3x
2 = 2·9
3x = 18Finally, we will Divide by 3 on each side to getThe solution to the equation is x = 6
Linear Equations Example 1
Find solutions to the equation:3x2 +4 = 13 Address fraction first
We can start by Subtracting 4 from each side3x2 = 3x
2 ����+4 − 4 = 13−4 = 93x2 = 9
Next, Multiply by 2 on each side3x = �2 · 3x
�2= 2·9
3x = 18Finally, we will Divide by 3 on each side to getThe solution to the equation is x = 6
Linear Equations Example 1
Find solutions to the equation:3x2 +4 = 13 Address fraction first
We can start by Subtracting 4 from each side3x2 = 3x
2 ����+4 − 4 = 13−4 = 93x2 = 9
Next, Multiply by 2 on each side3x = �2 · 3x
�2= 2·9 = 18
3x = 18Finally, we will Divide by 3 on each side to getThe solution to the equation is x = 6
Linear Equations Example 1
Find solutions to the equation:3x2 +4 = 13 Address fraction first
We can start by Subtracting 4 from each side3x2 = 3x
2 ����+4 − 4 = 13−4 = 93x2 = 9
Next, Multiply by 2 on each side3x = �2 · 3x
�2= 2·9 = 18
3x = 18
Finally, we will Divide by 3 on each side to getThe solution to the equation is x = 6
Linear Equations Example 1
Find solutions to the equation:3x2 +4 = 13 Address fraction first
We can start by Subtracting 4 from each side3x2 = 3x
2 ����+4 − 4 = 13−4 = 93x2 = 9
Next, Multiply by 2 on each side3x = �2 · 3x
�2= 2·9 = 18
3x = 18Finally, we will Divide by 3 on each side to get
The solution to the equation is x = 6
Linear Equations Example 1
Find solutions to the equation:3x2 +4 = 13 Address fraction first
We can start by Subtracting 4 from each side3x2 = 3x
2 ����+4 − 4 = 13−4 = 93x2 = 9
Next, Multiply by 2 on each side3x = �2 · 3x
�2= 2·9 = 18
3x = 18Finally, we will Divide by 3 on each side to get
3x3 = 18
3
The solution to the equation is x = 6
Linear Equations Example 1
Find solutions to the equation:3x2 +4 = 13 Address fraction first
We can start by Subtracting 4 from each side3x2 = 3x
2 ����+4 − 4 = 13−4 = 93x2 = 9
Next, Multiply by 2 on each side3x = �2 · 3x
�2= 2·9 = 18
3x = 18Finally, we will Divide by 3 on each side to get
x = �3x�3
= 183
The solution to the equation is x = 6
Linear Equations Example 1
Find solutions to the equation:3x2 +4 = 13 Address fraction first
We can start by Subtracting 4 from each side3x2 = 3x
2 ����+4 − 4 = 13−4 = 93x2 = 9
Next, Multiply by 2 on each side3x = �2 · 3x
�2= 2·9 = 18
3x = 18Finally, we will Divide by 3 on each side to get
x = �3x�3
= 183 = 6
The solution to the equation is x = 6
Linear Equations Example 1
Find solutions to the equation:3x2 +4 = 13 Address fraction first
We can start by Subtracting 4 from each side3x2 = 3x
2 ����+4 − 4 = 13−4 = 93x2 = 9
Next, Multiply by 2 on each side3x = �2 · 3x
�2= 2·9 = 18
3x = 18Finally, we will Divide by 3 on each side to get
x = �3x�3
= 183 = 6
The solution to the equation is x = 6
Linear Equations Example 1 Return to original problem
Find solutions to the equation:3x2 +4 = 13
To get rid of the fraction first we can Mulitply by 2 first.On the left, we distribute and multiply each term by 2.
3x + 8 = 26Next, we can Subtract 8 on both sides
3x = 18Finally, we will Divide by 3 on each side to getThe solution to the equation is x = 6
Linear Equations Example 1 Return to original problem
Find solutions to the equation:3x2 +4 = 13
To get rid of the fraction first we can Mulitply by 2 first.
On the left, we distribute and multiply each term by 2.3x + 8 = 26
Next, we can Subtract 8 on both sides3x = 18
Finally, we will Divide by 3 on each side to getThe solution to the equation is x = 6
Linear Equations Example 1 Return to original problem
Find solutions to the equation:3x2 +4 = 13
To get rid of the fraction first we can Mulitply by 2 first.2 ·(
3x2 +4
)= 2·13
On the left, we distribute and multiply each term by 2.3x + 8 = 26
Next, we can Subtract 8 on both sides3x = 18
Finally, we will Divide by 3 on each side to getThe solution to the equation is x = 6
Linear Equations Example 1 Return to original problem
Find solutions to the equation:3x2 +4 = 13
To get rid of the fraction first we can Mulitply by 2 first.2 ·(
3x2 +4
)= 2·13 = 26
On the left, we distribute and multiply each term by 2.3x + 8 = 26
Next, we can Subtract 8 on both sides3x = 18
Finally, we will Divide by 3 on each side to getThe solution to the equation is x = 6
Linear Equations Example 1 Return to original problem
Find solutions to the equation:3x2 +4 = 13
To get rid of the fraction first we can Mulitply by 2 first.2 ·(
3x2 +4
)= 2·13 = 26
On the left, we distribute and multiply each term by 2.
3x + 8 = 26Next, we can Subtract 8 on both sides
3x = 18Finally, we will Divide by 3 on each side to getThe solution to the equation is x = 6
Linear Equations Example 1 Return to original problem
Find solutions to the equation:3x2 +4 = 13
To get rid of the fraction first we can Mulitply by 2 first.2 ·(
3x2 +4
)= 2·13 = 26
On the left, we distribute and multiply each term by 2.2 · 3x
2 + 2·4 = 2 ·(
3x2 +4
)= 2·13 = 26
3x + 8 = 26Next, we can Subtract 8 on both sides
3x = 18Finally, we will Divide by 3 on each side to getThe solution to the equation is x = 6
Linear Equations Example 1 Return to original problem
Find solutions to the equation:3x2 +4 = 13
To get rid of the fraction first we can Mulitply by 2 first.2 ·(
3x2 +4
)= 2·13 = 26
On the left, we distribute and multiply each term by 2.3x + 8 = �2 · 3x
�2+ 2·4︸︷︷︸
8
= 2 ·(
3x2 +4
)= 2·13 = 26
3x + 8 = 26Next, we can Subtract 8 on both sides
3x = 18Finally, we will Divide by 3 on each side to getThe solution to the equation is x = 6
Linear Equations Example 1 Return to original problem
Find solutions to the equation:3x2 +4 = 13
To get rid of the fraction first we can Mulitply by 2 first.2 ·(
3x2 +4
)= 2·13 = 26
On the left, we distribute and multiply each term by 2.3x + 8 = �2 · 3x
�2+ 2·4︸︷︷︸
8
= 2 ·(
3x2 +4
)= 2·13 = 26
3x + 8 = 26
Next, we can Subtract 8 on both sides3x = 18
Finally, we will Divide by 3 on each side to getThe solution to the equation is x = 6
Linear Equations Example 1 Return to original problem
Find solutions to the equation:3x2 +4 = 13
To get rid of the fraction first we can Mulitply by 2 first.2 ·(
3x2 +4
)= 2·13 = 26
On the left, we distribute and multiply each term by 2.3x + 8 = �2 · 3x
�2+ 2·4︸︷︷︸
8
= 2 ·(
3x2 +4
)= 2·13 = 26
3x + 8 = 26Next, we can Subtract 8 on both sides
3x = 18Finally, we will Divide by 3 on each side to getThe solution to the equation is x = 6
Linear Equations Example 1 Return to original problem
Find solutions to the equation:3x2 +4 = 13
To get rid of the fraction first we can Mulitply by 2 first.2 ·(
3x2 +4
)= 2·13 = 26
On the left, we distribute and multiply each term by 2.3x + 8 = �2 · 3x
�2+ 2·4︸︷︷︸
8
= 2 ·(
3x2 +4
)= 2·13 = 26
3x + 8 = 26Next, we can Subtract 8 on both sides
3x + 8−8 = 26−8
3x = 18Finally, we will Divide by 3 on each side to getThe solution to the equation is x = 6
Linear Equations Example 1 Return to original problem
Find solutions to the equation:3x2 +4 = 13
To get rid of the fraction first we can Mulitply by 2 first.2 ·(
3x2 +4
)= 2·13 = 26
On the left, we distribute and multiply each term by 2.3x + 8 = �2 · 3x
�2+ 2·4︸︷︷︸
8
= 2 ·(
3x2 +4
)= 2·13 = 26
3x + 8 = 26Next, we can Subtract 8 on both sides
3x = 3x + 8−8 = 26−8
3x = 18Finally, we will Divide by 3 on each side to getThe solution to the equation is x = 6
Linear Equations Example 1 Return to original problem
Find solutions to the equation:3x2 +4 = 13
To get rid of the fraction first we can Mulitply by 2 first.2 ·(
3x2 +4
)= 2·13 = 26
On the left, we distribute and multiply each term by 2.3x + 8 = �2 · 3x
�2+ 2·4︸︷︷︸
8
= 2 ·(
3x2 +4
)= 2·13 = 26
3x + 8 = 26Next, we can Subtract 8 on both sides
3x = 3x + 8−8 = 26−8 = 18
3x = 18Finally, we will Divide by 3 on each side to getThe solution to the equation is x = 6
Linear Equations Example 1 Return to original problem
Find solutions to the equation:3x2 +4 = 13
To get rid of the fraction first we can Mulitply by 2 first.2 ·(
3x2 +4
)= 2·13 = 26
On the left, we distribute and multiply each term by 2.3x + 8 = �2 · 3x
�2+ 2·4︸︷︷︸
8
= 2 ·(
3x2 +4
)= 2·13 = 26
3x + 8 = 26Next, we can Subtract 8 on both sides
3x = 3x + 8−8 = 26−8 = 183x = 18
Finally, we will Divide by 3 on each side to getThe solution to the equation is x = 6
Linear Equations Example 1 Return to original problem
Find solutions to the equation:3x2 +4 = 13
To get rid of the fraction first we can Mulitply by 2 first.2 ·(
3x2 +4
)= 2·13 = 26
On the left, we distribute and multiply each term by 2.3x + 8 = �2 · 3x
�2+ 2·4︸︷︷︸
8
= 2 ·(
3x2 +4
)= 2·13 = 26
3x + 8 = 26Next, we can Subtract 8 on both sides
3x = 3x + 8−8 = 26−8 = 183x = 18
Finally, we will Divide by 3 on each side to get
The solution to the equation is x = 6
Linear Equations Example 1 Return to original problem
Find solutions to the equation:3x2 +4 = 13
To get rid of the fraction first we can Mulitply by 2 first.2 ·(
3x2 +4
)= 2·13 = 26
On the left, we distribute and multiply each term by 2.3x + 8 = �2 · 3x
�2+ 2·4︸︷︷︸
8
= 2 ·(
3x2 +4
)= 2·13 = 26
3x + 8 = 26Next, we can Subtract 8 on both sides
3x = 3x + 8−8 = 26−8 = 183x = 18
Finally, we will Divide by 3 on each side to get3x3 = 18
3
The solution to the equation is x = 6
Linear Equations Example 1 Return to original problem
Find solutions to the equation:3x2 +4 = 13
To get rid of the fraction first we can Mulitply by 2 first.2 ·(
3x2 +4
)= 2·13 = 26
On the left, we distribute and multiply each term by 2.3x + 8 = �2 · 3x
�2+ 2·4︸︷︷︸
8
= 2 ·(
3x2 +4
)= 2·13 = 26
3x + 8 = 26Next, we can Subtract 8 on both sides
3x = 3x + 8−8 = 26−8 = 183x = 18
Finally, we will Divide by 3 on each side to getx = �3x
�3= 18
3
The solution to the equation is x = 6
Linear Equations Example 1 Return to original problem
Find solutions to the equation:3x2 +4 = 13
To get rid of the fraction first we can Mulitply by 2 first.2 ·(
3x2 +4
)= 2·13 = 26
On the left, we distribute and multiply each term by 2.3x + 8 = �2 · 3x
�2+ 2·4︸︷︷︸
8
= 2 ·(
3x2 +4
)= 2·13 = 26
3x + 8 = 26Next, we can Subtract 8 on both sides
3x = 3x + 8−8 = 26−8 = 183x = 18
Finally, we will Divide by 3 on each side to getx = �3x
�3= 18
3 = 6
The solution to the equation is x = 6
Linear Equations Example 1 Return to original problem
Find solutions to the equation:3x2 +4 = 13
To get rid of the fraction first we can Mulitply by 2 first.2 ·(
3x2 +4
)= 2·13 = 26
On the left, we distribute and multiply each term by 2.3x + 8 = �2 · 3x
�2+ 2·4︸︷︷︸
8
= 2 ·(
3x2 +4
)= 2·13 = 26
3x + 8 = 26Next, we can Subtract 8 on both sides
3x = 3x + 8−8 = 26−8 = 183x = 18
Finally, we will Divide by 3 on each side to getx = �3x
�3= 18
3 = 6The solution to the equation is x = 6
