Types of Solutions Types of Solutions Types of Solutions Types of Solutions when Solving when Solving when Solving when Solving

MultiMultiMultiMulti----Step Equations Step Equations Step Equations Step Equations FoldableFoldableFoldableFoldable

Topic: “Types of Solutions when

Solving Multi-Step Equations ”

One Solution

InfiniteSolution

No Solution

Instructions:Cut on dotted lines. Fold on solid lines.

You will create a 6 door foldable. Glue/Tape this side face down in your notebook.

What does One SolutionOne SolutionOne SolutionOne Solution mean?

What does Infinite Solutions Infinite Solutions Infinite Solutions Infinite Solutions mean?

What does No SolutionNo SolutionNo SolutionNo Solution mean?

Solve: 3(2x + 4) = 6(5x + 2)

Solve: 3(x + 1) + 1 + 2x = 2(2x + 2) + x

Solve: 8x + 3 – 10x = -2(x – 2) + 3

Check:

Check:

Check:

Topic: “Types of Solutions when

Solving Multi-Step Equations ”

One Solution

InfiniteSolution

No SolutionAnswer Key

Instructions:Cut on dotted lines. Fold on solid lines.

You will create a 6 door foldable. Glue/Tape this side face down in your notebook.

What does One SolutionOne SolutionOne SolutionOne Solution mean?

If an equation has only one solution, no other numbers

except that one solution will work in this equation.

What does Infinite Solutions Infinite Solutions Infinite Solutions Infinite Solutions mean?If an equation has infinite solutions, any number will work as a solution. It doesn’t matter which number you pick! Every number you can think of will work as a solution when you

check this equation.

What does No SolutionNo SolutionNo SolutionNo Solution mean?

If an equation has no solution, no numbers will work as an answer to this equation.

Solve: 3(2x + 4) = 6(5x + 2)

6x + 12 = 30x + 12-6x -6x

12 = 24x + 12-12 -120 = 24x24 240 = x

Solve: 3(x + 1) + 1 + 2x = 2(2x + 2) + x

3x + 3 + 1 + 2x = 4x + 4 + x5x + 4 = 5x + 4-5x -5x

4 = 4

Infinite Solutions!

Solve: 8x + 3 – 10x = -2(x – 2) + 3

8x + 3 -10x = -2x + 4 + 3-2x + 3 = -2x + 7+ 2x + 2x

3 ≠ 7

No Solution

Check:3(2(0)+4) = 6(5(0) + 2)3(0 + 4) = 6(0 + 2) 3(4) = 6(2)12 = 12�

Check: (Check Two Times!)Pick any 2 numbers. Both will work

x = 03(0+1)+1+2(0)=2(2(0) + 2) + 0

3(1)+1+0 = 2(0+2)3+1=2(2)4=4�

x = 13(1+1)+1+2(1)=2(2(1) + 2) + 1

3(2)+1+2 = 2(2+2) + 16+3=2(4) + 1

9=9�

Check:

Answer Key

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