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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 28 Page 143

Start by multiplying both sides by - 3.

z = - 3/2

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 multiplying both sides by - 3. This way we will eliminate the fraction.

- 1/3(4+z)=- 5/6

MoveNegFracToDenom

Put minus sign in denominator

1/- 3(4+z)=- 5/6

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

- 3 * 1/- 3(4+z)=(- 3)(- 5/6)

NumberToDenomMultFrac

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

1(4+z)=(- 3)(- 5/6)

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Simplify left-hand side

Identity Property of Multiplication

(4+z)=(- 3)(- 5/6)

Remove parentheses

4+z=(- 3)(- 5/6)

▼

Simplify right-hand side

MultNegNegTwoPar

(- a)(- b)=a* b

4+z= 3 * 5/6

MoveLeftFacToNum

a*b/c= a* b/c

4+z= 3 * 5/6

Multiply

4+z= 15/6

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

4+z= 15/3/6/3

Calculate quotient

4+z= 5/2

CommutativePropAdd

Commutative Property of Addition

z+4= 5/2

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

z+4= 5/2

LHS-4=RHS-4

z+4-4= 5/2-4

Subtract term

z= 5/2-4

Rewrite 4 as 8/2

z= 5/2-8/2

Subtract fractions

z = 5-8/2

Subtract term

z = - 3/2

MoveNegNumToFrac

Put minus sign in front of fraction

z = - 3/2

The solution to the equation is z = - 32. We can check our solution by substituting it into the original equation.

- 1/3(4+z)=- 5/6

z= - 3/2

- 1/3(4+( - 3/2)) ? = - 5/6

▼

Simplify

a+(- b)=a-b

- 1/3(4- 3/2) ? = - 5/6

Rewrite 4 as 8/2

- 1/3(8/2- 3/2) ? = - 5/6

Subtract fractions

- 1/3 * 8-3/2 ? = - 5/6

Subtract term

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

Multiply fractions

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

Multiply

- 5/6=- 5/6

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