NOTES: Equations w/Distributive Property

​Solving Equations with Distribution

​Algebra 1

​Ms. Rico

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WARM-UP:

Solve $$24=15-3x$$  

Distributive Property​

• The Distributive Property means to multiply the number outside the parentheses with each number inside the parentheses. Then simplify and solve.

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• Distirbute means to multiply. One way to remember distributive property is to think about a "Rainbow" or multiply the outside number with each number on the inside.

​Example 1

​Example 2

​Example 3

​Example 4

​Example 5

Multiple Choice

Use the distributive Property. Which is the correct answer?

  $$2\left(x+3\right)$$  

• $$2x+3$$  

• $$2x+6$$  

• $$2x+5$$  

Multiple Choice

Use the distributive Property. Which is the correct answer?

  $$-4\left(-4x-5\right)$$  

•   $$-16x+20$$  

•   $$16+20$$  

•   $$16x+20$$  

•   $$16x-20$$  

Multiple Choice

Use the distributive Property. Which is the correct answer?

  $$-\left(x-8\right)$$  

• $$-x-8$$  

•   $$-x+8$$  

• $$x+8$$  

Steps for Solving Two-Step equations with Distribution

​Step 1: Distribute

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Step 2: Use inverse operations to Add or Subtract

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Step 3: Use inverse operations to Multiply or Divide

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Step 4: Variable should be by itself. Woo Hoo!!!

​Example 6

​Example 7

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Use the distributive Property. What is the value of x?

  $$2\left(x+2\right)=26$$  

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Solve for x.

  $$24=4\left(x+2\right)$$  

​Example 8

​Example 9

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Solve for x.

  $$-3\left(7x-5\right)=99$$  

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Solve for x.

  $$-10=-5\left(-4x+1\right)$$  

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Solve for x.

  $$-5\left(7x-9\right)-6=144$$  

​Example 10

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Solve for x.

  $$-\left(5x-8\right)=-22$$