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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

Practice Test

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Exercise 6 Page 176

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

k=- 7

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, we need to start by using the Addition Property of Equality to simplify the left- and right-hand sides of the equation.

2/7k-3/8=- 19/8

LHS+3/8=RHS+3/8

2/7k-3/8+3/8=- 19/8+3/8

Add terms

2/7k=- 19/8+3/8

MoveNegFracToNum

Put minus sign in numerator

2/7k=- 19/8+3/8

Add terms

2/7k=- 19+3/8

Add terms

2/7k=- 16/8

Next, we can use the Multiplication Property of Equality to simplify the equation even further,

2/7k=- 16/8

LHS * 7/2=RHS* 7/2

2/7k* 7/2=- 16/8* 7/2

▼

Simplify left-hand side

CommutativePropMult

Commutative Property of Multiplication

2/7* 7/2k=- 16/8* 7/2

MultFracByInverse

a/b* b/a=1

1k=- 16/8* 7/2

Identity Property of Multiplication

k=- 16/8* 7/2

Multiply fractions

k=- 16* 7/8* 2

Multiply

k=- 112/16

MoveNegNumToFrac

Put minus sign in front of fraction

k=-112/16

Calculate quotient

k=- 7

The solution to the equation is k=- 7. We can check our solution by substituting it into the original equation.

2/7k-3/8=- 19/8

k= - 7

2/7( - 7)-3/8? =- 19/8

▼

Simplify

MoveRightFacToNum

a/c* b = a* b/c

2(- 7)/7-3/8? =- 19/8

a(- b)=- a * b

- 2(7)/7-3/8? =- 19/8

Multiply

- 14/7-3/8? =- 19/8

a/b=a * 8/b * 8

- 112/56-3/8? =- 19/8

a/b=a * 7/b * 7

- 112/56-21/56? =- 19/8

Subtract fractions

- 112-21/56? =- 19/8

Subtract term

- 133/56? =- 19/8

a/b=.a /7./.b /7.

- 19/8? =- 19/8

MoveNegNumToFrac

Put minus sign in front of fraction

- 19/8=- 19/8

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

Extra

Learn More!

Are you having trouble learning how to solve equations? Would you like to see why the Properties of Equality work? Do real-world examples help you understand more about the why and how of math topics? If you answered Yes to any of these questions, check out the Mathleaks courses related to this topic!