Solving Multistep Equations.

When you have an equation with Variables AND constants on both sides, you need to make a decision to put only the variable on one side, and the constant on the other.

3x + 1 = 2x + 5

-1 -1

3x = 2x + 4

-2x -2x

So x =

• 4

• 5

• 1

• -1

Answer explanation

3x + 1 = 2x + 5

A good strategy is to remove the "smaller" amount of x's (2x) from both sides.

x + 1 = 5

This leaves a very simple problem: x = 4

6a + 2 = 4a + 8

a =

• a = 4

• a = 3

• a = 2

• a = 1

Answer explanation

6a + 2 = 4a + 8

After you solve it (a = 3), CHECK by substituting a = 3 into the equation.

6(3) + 2 = 4(3) + 8

18 + 2 = 12 + 8

20 = 20 Check!

6a + 6 = 12a + 24

• a = 3

• a = -3

• a = 1

• a = -1

5x - 10 = 2x + 2

• x = -2

• x = 2

• x = 4

• x = -4

4x + 1 = 2x + 7

• x = 1

• x = 3

• x = -1

• x = - 3

3(2x + 1) = 2x + 19

When you have an equation with parenthesis, you have to distribute first:

The left side becomes 6x + 3.

The whole equation becomes 6x + 3 = 2x + 19.

Solve 6x + 3 = 2x + 19

• x = 2

• x = 4

• x = 3

• x = 1

2(x + 3) = x + 8

• x = 1

• x = 2

• x = -2

• x = -1

4(x + 1) = x + 10

• x = -1

• x = 2

• x = 8

• x = 1

When you have parenthesis on BOTH sides of the equation, distribute on both sides.

2(3x + 5) = 4(x + 5)

6x + 10 = 4x + 20

And then solve for x.

• x = 5

• x = 2

• x = 10

• x = 3

5(x + 1) = 4(x + 2)

• x = 2

• x = 3

• x = -3

• x = -4