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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 29 Page 143

Start by subtracting 2 from both sides.

b = 13 12

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 2 from both sides.

2-b/3=- 5/2

CommutativePropAdd

Commutative Property of Addition

- b/3+2=- 5/2

LHS-2=RHS-2

- b/3+2-2=- 5/2-2

Subtract term

- b/3=- 5/2-2

▼

Simplify right-hand side

Rewrite 2 as 4/2

- b/3=- 5/2-4/2

MoveNegFracToNum

Put minus sign in numerator

- b/3=- 5/2-4/2

Subtract fractions

- b/3=- 5 -4/2

Subtract term

- b/3=- 9/2

Now, we are going to multiply the equation by - 3 using the Multiplication Property of Equality to eliminate the fraction. Let's go!

- b/3=- 9/2

MoveNegFracToDenom

Put minus sign in denominator

b/- 3=- 9/2

LHS * (- 3)=RHS* (- 3)

b/- 3 * (- 3) =- 9/2 * (- 3)

FracMultDenomToNumber

a/(- 3)* (- 3) = a

b =- 9/2 * (- 3)

MoveRightFacToNum

a/c* b = a* b/c

b =- 9(- 3)/2

▼

Multiply

MultNegNegOnePar

- a(- b)=a* b

b =9 * 3/2

Multiply

b =27/2

Write fraction as a mixed number

b = 13 12

The solution to the equation is b = 13 12. We can check our solution by substituting it into the original equation.

2-b/3=- 5/2

b= 13 12

2-13 12/3 ? = - 5/2

▼

Simplify

a bc=a* c+b/c

2-13 * 2 + 12/3 ? = - 5/2

Multiply

2-26 + 12/3 ? = - 5/2

Add terms

2-272/3 ? = - 5/2

a/c/b= a/b* c

2-27/3 * 2 ? = - 5/2

Multiply

2-27/6 ? = - 5/2

Rewrite 2 as 12/6

12/6-27/6 ? = - 5/2

Subtract fractions

12-27/6 ? = - 5/2

Subtract term

- 15/6 ? = - 5/2

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

- 15/3/6/3 ? = - 5/2

Calculate quotient

- 5/2 ? = - 5/2

MoveNegNumToFrac

Put minus sign in front of fraction

- 5/2=- 5/2

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