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Big Ideas Math: Modeling Real Life, Grade 7

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Big Ideas Math: Modeling Real Life, Grade 7 View details

3. Solving Two-Step Equations

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Exercise 27 Page 143

Start by adding 56 to both sides.

a = 1 13

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, the only variable term is already on the left-hand side of the equation, so we will start by adding 56 to both sides.

a/4-5/6=- 1/2

LHS+5/6=RHS+5/6

a/4-5/6+5/6=- 1/2+5/6

▼

Add terms

a+(- b)=a-b

a/4+(- 5/6)+5/6=- 1/2+5/6

MoveNegFracToNum

Put minus sign in numerator

a/4+ - 5/6+5/6=- 1/2+5/6

a/b=a * 3/b * 3

a/4+ - 5/6+5/6=- 1 * 3/2 * 3+5/6

Multiply

a/4+ - 5/6+5/6=- 3/6+5/6

Add fractions

a/4+ - 5+5/6=- 3+5/6

Add terms

a/4+ 0/6=2/6

0/a=0

a/4+ 0=2/6

Identity Property of Addition

a/4=2/6

a/b=.a /2./.b /2.

a/4=2/2/6/2

Calculate quotient

a/4=1/3

Now, we are going to multiply the equation by 4 using the Multiplication Property of Equality to get rid of the fraction. Let's go!

a/4=1/3

LHS * 4=RHS* 4

a/4 * 4= 1/3 * 4

FracMultDenomToNumber

a/4* 4 = a

a= 1/3 * 4

MoveRightFacToNumOne

1/b* a = a/b

a = 4/3

Write fraction as a mixed number

a = 1 13

The solution to the equation is a = 1 13. We can check our solution by substituting it into the original equation.

a/4-5/6=- 1/2

a= 1 13

1 13/4-5/6 ? = - 1/2

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Simplify

a bc=a* c+b/c

1* 3+13/4-5/6 ? = - 1/2

Identity Property of Multiplication

3+13/4-5/6 ? = - 1/2

Add terms

43/4-5/6 ? = - 1/2

a/c/b= a/b* c

4/4 * 3-5/6 ? = - 1/2

Multiply

4/12-5/6 ? = - 1/2

a/b=.a /2./.b /2.

4/2/12/2-5/6 ? = - 1/2

Calculate quotient

2/6-5/6 ? = - 1/2

Subtract fractions

2-5/6? = - 1/2

Subtract term

- 3/6? = - 1/2

MoveNegNumToFrac

Put minus sign in front of fraction

-3/6? = - 1/2

a/b=.a /3./.b /3.

-3/3/6/3? = - 1/2

Calculate quotient

- 1/2=- 1/2

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

Subchapter links

Try It p.140-141

Self-Assessment for Concept & Skills p.141

Self-Assessment for Problem Solving p.142

Review & Refresh p.143

Concept, Skills, & Problem Solving p.143-144