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Big Ideas Math Geometry, 2014

BI

Big Ideas Math Geometry, 2014 View details

Maintaining Mathematical Proficiency

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Exercise 7 Page 63

Use inverse operations until you have fully isolated x.

x=y-5

Practice makes perfect

To solve the given literal equation for x, we will use the Properties of Equality to apply inverse operations on the equation. Remember, only like terms can be combined. Since the inverse operation to addition is subtraction, to eliminate 2y we have to subtract 2y from both sides of the equation.

2y-2x=10

LHS-2y=RHS-2y

2y-2x - 2y=10 - 2y

Subtract terms

- 2x=10-2y

Next, we will eliminate the minus sign from the left-hand side of the equation. This will make the further transformations easier.

- 2x=10-2y

LHS * (- 1)=RHS* (- 1)

- 2x( - 1)=(10-2y)( - 1)

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Simplify

MultNegNegOnePar

- a(- b)=a* b

2x=(10-2y)(- 1)

Distribute - 1

2x=- 10+2y

CommutativePropAdd

Commutative Property of Addition

2x=2y-10

Finally, we have to eliminate 2 from in front of x. Division is the inverse operation to multiplication, so we have to divide both sides of the equation by 2.

2x=2y-10

.LHS /2.=.RHS /2.

2x/2= 2y-10/2

Calculate quotient

x=2y-10/2

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Simplify right-hand side

Write as a difference of fractions

x=2y/2-10/2

Calculate quotient

x=y-5

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Exercises p.63