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Big Ideas Math: Modeling Real Life, Grade 8

BI

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

3. Solving Equations with Variables on Both Sides

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Exercise 12 Page 22

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

k=- 3/4

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.

3k-1=7k+2

LHS-7k=RHS-7k

3k-1-7k=7k+2-7k

Subtract terms

-4k-1=2

LHS+1=RHS+1

-4k-1+1=2+1

Add terms

-4k=3

.LHS /(-4).=.RHS /(-4).

-4k/-4=3/-4

- a/- b=a/b

4k/4=3/-4

MoveNegDenomToFrac

Put minus sign in front of fraction

4k/4=- 3/4

Calculate quotient

k=- 3/4

The solution to the equation is k=- 34. We can check our solution by substituting it into the original equation.

3k-1=7k+2

k= - 34

3( - 3/4)-1 ? = 7( - 3/4)+2

▼

Simplify

a(- b)=- a * b

- 3(3/4)-1 ? = -7(3/4)+2

MoveLeftFacToNum

a*b/c= a* b/c

- 9/4-1? =- 21/4+2

a = 4* a/4

- 9/4-4/4 ? =- 21/4+8/4

Add and subtract terms

- 13/4= - 13/4

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