Solving Multi-Step Equations Involving CLT and Distribution

Solving Multi-Step Equations Involving CLT and Distribution

By the end of this lesson you will be able to solve linear equations that involve both distribution and combining like terms

DCI is used to remember the order of the steps for solving these multi-step equations

Distribute

Combine Like Terms

Inverse Operations

Steps:

• Distribute wherever there are parantheses

• Combine like terms on each side of the equation

• Inverse Operations to solve for the variable

• Check your work

Example 1:

Solve the equation to the right.

Remember DCI!

Step 1: Distribute

The D of DCI



You need to distribute 8 to all terms within the parantheses

Step 2: Combine like terms

This is the C of DCI

The left side does not have any like terms so it is "cleaned up"

The right side has an 8x and a -5x which will combine to 3x

Step 3: Solve Using Inverse Operations

The I of DCI

Move all your variables to one side and constants to the other side. Then solve for the variable....

Step 4: Check

substitute your answer into all variables in the original equation

Example 2:

Remember DCI!

D: Distribute the -4 first

C: Combine like terms on left

I: Inverse Operations - subtract 4 from both sides and then divide by them both by -4

Multiple Choice

Solve the Equation: -3(x - 1) + 7x = -9

• -2

• 2

• -3

• 3

Multiple Choice

Solve the equation: -2(n + 3) = 4n - 3

• -2

• 2

• -1/2

• 1/2