+

Algebra 2

Miss Hudson’s Maths

+ Solving EquationsThe aim is to find the value of the variable that makes the mathematical sentence true.

To do this we need to step by step strip all other terms away from the variable (usually x) ie isolate the x

What you do to one side, you do to the other in order to keep the sides balanced.

eg 1: 6x = 186

To strip terms away - do the

opposite!

6

x = 3

eg 2: x - 4 = 7+ 4 + 4

x = 11

eg 3: x7

= 3x 7x 7

x = 21

Miss Hudson’s Maths

+eg 4: 2x - 5 = 3

+ 5+ 5

2x = 822

x = 4

eg 5: (gives a negative answer)

2x + 15 = 1-15 -15

2x = -1422

x = -7

eg 6: (gives a fractional answer)

6x + 1 = 9-1-1

6x = 866

x = 43

or 1 13

Miss Hudson’s Maths

+eg 7: 3

x - 4 = - 3+4 +4

x3

= 1x 3x 3

x = 3

eg 8: 2 x - 43

= -2x 3x 3

2 x - 4 = -6+ 4+ 4

2 x = - 22 2

x = - 1

Miss Hudson’s Maths

+Equations with Brackets

eg 9: 3 ( 2 y - 1 ) = 21

Expand the brackets first; so we go 3 x 2y and 3 x -1 =

6 y - 3 = 21+ 3+ 3

6 y = 2466

y = 4

Miss Hudson’s Maths

+ If x appears on both sides of the equation we need to collect all the x’s on the side that has most of them first.

eg 10: 5x = 3x + 8-3x -3x

2x = 82 2

x = 4

eg 11: -4x + 8 = 2x - 20+ 4x+ 4x

8 = 6x - 20+ 20 + 20

28 = 6x6 6

= x

Collect the numbers on

the other side

4⅔Miss Hudson’s Maths

+Writing Equations & Solving Themeg 1: I am thinking of a number. If I multiply this number by 3, I get a result of 18. What is the number?Solution:

Let the number be x3x = 18

x = 6The number is 6

eg 2: When 4 times a number is added to 5 the result is 17. Find the original number by forming an equation and solving it.

Let the number be nSolution: 4n + 5 = 17

4n = 124 4n = 3

The number is 3

3 3

-5 -5

Miss Hudson’s Maths

+eg 3: Twice a certain number is 7 more than the number. What is the number?Solution

:Let the number be x

2x = x + 7-x-x

x = 7The number is 7

eg 4: When 3 times a number is added to the original number the result is 16. Find the original number by forming an equation and solving it.

Let the number be nSolution: 3n + n = 16

4n = 164 4n = 4

The number is 4 Miss Hudson’s Maths

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Eight is added to the number n.

Six is added to three times the number n.

Four is added to five times a certain number x.

Thirty is subtracted from six times a certain number y.

A certain number m is multiplied by negative five and then eight is added.

A certain number q is divided by four and then six is added.

Twelve is divided by negative x.

The number x is multiplied by negative three and the result is divided by five.

Four times the number z is subtracted from negative three.

Three times the number y is divided into negative twelve. Miss Hudson’s Maths