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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 6 Page 94

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

x=5/2

Practice makes perfect

To solve an equation, we should first gather all of the variable terms on one side of the equation and all of the constant terms on the other side using inverse operations. In this case, we need to start by adding 25x to both sides of the equation to isolate the x-terms on the right side.

- 2/5x+3=2/3x+1/3

LHS+ 2/5x=RHS+ 2/5x

- 2/5x+3+ 2/5x=2/3x+1/3+ 2/5x

▼

Simplify

a/b=a * 5/b * 5

- 2/5x+3+2/5x=2* 5/3* 5x+1/3+2/5x

a/b=a * 3/b * 3

- 2/5x+3+2/5x=2* 5/3* 5x+1/3+2* 3/5* 3x

Multiply

- 2/5x+3+2/5x=10/15x+1/3+6/15x

CommutativePropAdd

Commutative Property of Addition

- 2/5x+2/5x+3=10/15x+6/15x+1/3

MoveRightFacToNum

a/c* b = a* b/c

- 2x/5+2x/5+3=10x/15+6x/15+1/3

MoveNegFracToNum

Put minus sign in numerator

- 2x/5+2x/5+3=10x/15+6x/15+1/3

Add fractions

- 2x+2x/5+3=10x+6x/15+1/3

Add terms

3=16x/15+1/3

Now, we will subtract 13 from both sides of the equation to isolate the constant terms on its left-hand side.

3=16x/15+1/3

LHS- 1/3=RHS- 1/3

3- 1/3=16x/15+1/3- 1/3

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Simplify

a = 3* a/3

3* 3/3-1/3=16x/15+1/3-1/3

Multiply

9/3-1/3=16x/15+1/3-1/3

Subtract fractions

9-1/3=16x/15+1-1/3

Subtract terms

8/3=16x/15

Finally, we can multiply both sides of the equation by 1516. It is an inverse of the fraction standing next to the variable.

8/3=16x/15

LHS * 15/16=RHS* 15/16

8/3* 15/16=16x/15* 15/16

▼

Multiply fractions

CommutativePropMult

Commutative Property of Multiplication

8/3* 15/16=16/15* 15/16* x

MultFracByInverse

a/b* b/a=1

8/3* 15/16=1* x

Multiply fractions

8* 15/3* 16=1* x

Multiply

120/48=x

a/b=.a /24./.b /24.

5/2=x

Rearrange equation

x=5/2

The solution to the equation is x= 52.

Subchapter links

Do You Understand? p.94

Do You Know How? p.94

Practice & Problem Solving p.95-96

Assessment Practice p.96