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Big Ideas Math: Modeling Real Life, Grade 7

BI

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

3. Solving Two-Step Equations

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Exercise 31 Page 143

Start by subtracting 45 from both sides.

v= -1/30

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 subtracting 45 from both sides.

- 9/4v+4/5= 7/8

LHS-4/5=RHS-4/5

- 9/4v+4/5-4/5= 7/8-4/5

▼

Subtract term

a/b=a * 5/b * 5

- 9/4v+4/5-4/5= 7 * 5/8 * 5-4/5

a/b=a * 8/b * 8

- 9/4v+4/5-4/5= 7 * 5/8 * 5-4 * 8/5 * 8

Multiply

- 9/4v+4/5-4/5= 35/40-32/40

Subtract fractions

- 9/4v+4-4/5= 35-32/40

Subtract term

- 9/4v+0/5= 3/40

0/a=0

- 9/4v+0=3/40

Identity Property of Addition

- 9/4v= 3/40

Now, we are going to multiply the equation by - 4, and then divide it by 9 using the Multiplication and Division Properties of Equality. This will help us get rid of the fraction. Let's go!

- 9/4v= 3/40

MoveRightFacToNum

a/c* b = a* b/c

- 9v/4= 3/40

MoveNegFracToDenom

Put minus sign in denominator

9v/- 4= 3/40

LHS * (- 4)=RHS* (- 4)

9v/- 4 * (- 4)= 3/40 * (- 4)

FracMultDenomToNumber

a/(- 4)* (- 4) = a

9v= 3/40 * (- 4)

▼

Simplify right-hand side

MoveRightFacToNum

a/c* b = a* b/c

9v= 3(- 4)/40

a(- b)=- a * b

9v =- 3* 4/40

Multiply

9v =- 12/40

Next, we will use the Division Property of Equality to simplify the equation even further.

9v =- 12/40

.LHS /9.=.RHS /9.

9v/9 = - 1240/9

a/c/b= a/b* c

9v/9 = - 12/9 * 40

Multiply

9v/9 = - 12/360

Calculate quotient

v=- 12/360

▼

Simplify right-hand side

MoveNegNumToFrac

Put minus sign in front of fraction

v=-12/360

a/b=.a /12./.b /12.

v=-12/12/360/12

Calculate quotient

v=-1/30

The solution to the equation is v= - 130. We can check our solution by substituting it into the original equation.

- 9/4v+4/5= 7/8

v= -1/30

- 9/4( -1/30) +4/5 ? = 7/8

▼

Simplify left-hand side

MultNegNegOnePar

- a(- b)=a* b

9/4 * 1/30 +4/5 ? = 7/8

Multiply fractions

9 * 1/4 * 30 +4/5 ? = 7/8

Multiply

9/120 +4/5 ? = 7/8

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

9/3/120/3 +4/5 ? = 7/8

Calculate quotient

3/40 +4/5 ? = 7/8

a/b=a * 8/b * 8

3/40 +4 * 8/5 * 8 ? = 7/8

Multiply

3/40 +32/40 ? = 7/8

Add fractions

35/40 ? = 7/8

a/b=.a /5./.b /5.

35/5/40/5 ? = 7/8

Calculate quotient

7/8=7/8

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