Solving Linear Equations Involving Combining Like Terms

Solving Linear Equations Involving Combining Like Terms

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

Steps:

• Identify and combine all like terms on the left side of the equation ("clean up" the left side)

• Identify and combine all like terms on the right side of the equation ("clean up" the right side)

• Solve using inverse operations

• Check your answer

Example:

Solve the equation 6n + 3 + 8n + 2 = 23

Step 1: Identify and combine like terms

"Clean up" the left side of the equation

6n + 3 + 8n + 2 = 23

(6n + 8n) + (3 + 2) = 23

14n + 5 = 23

Step 2: Identify and combine like terms

"Clean up" the right side of the equation

14n + 5 = 23 .... The right side has no like terms to combine

Step 3: Solve Using Inverse Operations

14n + 5 = 23 (subtract 5 from both sides)

14n = 18 (divide both sides by 14)

n = 18/14 which simplifies to 9/7

Check: Try 9/7 in the original equation

6(9/7) + 3 + 8(9/7) + 2 = 23

54/7 + 3 + 72/7 + 2 = 23

126/7 + 3 + 2 = 23

18 + 3 + 2 = 23

23 = 23 CHECKS!

Example: Solve the equation

8x + 7 - 10x = 10 + 3x + 12

Step 1: Identify and combine like terms

"Clean up" the left side of the equation

8x + 7 - 10x =

(8x - 10x) + 7 =

-2x + 7 =

Step 2: Identify and combine like terms

"Clean up" the right side of the equation

= 10 + 3x + 12

= 3x + (10 + 12)

= 3x + 22

Step 3: Solve Using Inverse Operations

-2x + 7 = 3x + 22 (add 2x to both sides)

7 = 5x + 22 (subtract 22 from both sides)

-15 = 5x (divide both sides by 5)

-3 = x or x = -3

Check: Try -3 in the original equation

8(-3) + 7 - 10(-3) = 10 + 3(-3) + 12

-24 + 7 + 30 = 10 + (-9) + 12

13 = 13 CHECKS!

Extra Example...

Multiple Choice

Solve the Equation: 3x + 5 - 7x + 9 = 20 + 6x - x + 12

• 2

• -2

• 18

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