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Envision Math 2.0: Grade 8, Volume 1

EM

Envision Math 2.0: Grade 8, Volume 1 View details

2. Solve Equations with Variables on Both Sides

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Exercise 12 Page 95

Gather all of the variable terms on one side of the equation and all of the constant terms on the other side.

x=4

Practice makes perfect

To solve an equation, we should first gather all of the variable terms on one side and all of the constant terms on the other side using inverse operations. In this case, we need to start by adding 6x to both sides of the equation to isolate the x-terms on the right-hand side.

6-6x=5x-9x-2

LHS+ 6x=RHS+ 6x

6-6x+ 6x=5x-9x-2+ 6x

CommutativePropAdd

Commutative Property of Addition

6-6x+6x=5x-9x+6x-2

Add and subtract terms

6=2x-2

Now, we will add 2 to both sides of the equation to isolate the constant terms on the left-hand side.

6=2x-2

LHS+ 2=RHS+ 2

6+ 2=2x-2+ 2

Add terms

8=2x

Finally, to solve the equation we should divide both sides by 2. It is the number standing next to the variable.

8=2x

▼

Solve for x

.LHS / 2.=.RHS / 2.

8 ÷ 2 = 2x ÷ 2

Calculate quotient

4=x

Rearrange equation

x=4

The solution to the equation is x=4.

Subchapter links

Do You Understand? p.94

Do You Know How? p.94

Practice & Problem Solving p.95-96

Assessment Practice p.96