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Big Ideas Math: Modeling Real Life, Grade 8

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Big Ideas Math: Modeling Real Life, Grade 8 View details

3. Solving Equations with Variables on Both Sides

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Exercise 18 Page 22

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 the Properties of Equality. In this case, we need to start by using the Distributive Property to simplify the right-hand sides of the equation.

0.1x=0.2(x+2)

Distribute 0.2

0.1x=0.2x+0.4

Now, we can continue to solve using the Properties of Equality.

0.1x=0.2x+0.4

LHS-0.2x=RHS-0.2x

0.1x-0.2x=0.2x+0.4-0.2x

Subtract terms

-0.1x=0.4

LHS * (-10)=RHS* (-10)

-0.1x(-10)=0.4(-10)

CommutativePropMult

Commutative Property of Multiplication

-0.1(-10)x=0.4(-10)

MultNegNegOnePar

- a(- b)=a* b

0.1(10)x=0.4(-10)

a(- b)=- a * b

0.1(10)x=- 0.4(10)

Multiply

x=- 4

The solution to the equation is x=-4. We can check our solution by substituting it into the original equation.

0.1x=0.2(x+2)

x= - 4

0.1( - 4) ? = 0.2( - 4+2)

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Simplify

Add terms

0.1(-4) ? = 0.2(-2)

a(- b)=- a * b

-0.4 = -0.4

Since the left-hand side is equal to the right-hand side, our solution is correct.

Subchapter links

Try It p.18-20

Self-Assessment for Concepts & Skills p.20

Self-Assessment for Problem Solving p.21

Review & Refresh p.22

Concepts, Skills, & Problem Solving p.22-24