Exercise 18 Page 288

We have been given a partially completed two-column proof. Consider the given statement and the desired result.

• Given: 1/5x+3=2x-24
• Prove: x=15

In order to complete the table, and prove that x=15, we will solve the equation. Before that we can fill in blank a in the Statements column based on the given information. & a. 1/5x+3=2x-24 & a. Given

Blank b

Now, we can start to solve the equation. We began by multiplying both sides of the equation by 5, which can be justified by the Multiplication Property of Equality.

& b. 5(1/5x+3)=5(2x-24) & b. Multiplication Property of Equality

Blank c

Let's continue with the next step of the proof.

5(1/5x+3)=5(2x-24)

Distr

Distribute 5

x+15=10x-120

Here, we distributed 5. Therefore, the property that justifies this step is the Distributive Property. & c. x+15=10x-120 & c. Distributive Property

Blank d

Let's continue solving the equation.

x+15=10x-120

SubEqn

LHS- x=RHS- x

x- x+15=10x- x-120

SubTerms

Subtract terms

15=9x-120

We are subtracted x from both sides of the equation by the Subtraction Property of Equality. Then, we and simplified the obtained equation. & d. 15=9x-120 & d. Subtraction Property of Equality

Blank e

Let's focus on the next step.

15=9x-120

AddEqn

LHS+ 120=RHS+ 120

15+ 120=9x-120+ 120

AddTerms

Add terms

135=9x

In this step, we added 120 to both sides of the equation and simplified the obtained equation. This means that we used the Addition Property of Equality. & e. 135=9x & e. Addition Property of Equality

Blank f

We are almost done!

135=9x

DivEqn

.LHS / 9.=.RHS / 9.

135/9=9x/9

CalcQuot

Calculate quotient

15=x

By the Division Property of Equality, we divided both sides of the equation by 9. & f. 15=x & f. Division Property of Equality

Blank g

Now, we will fill in the last blank and complete the proof.

15=x

RearrangeEqn

Rearrange equation

x=15

We rearranged the equation by the Symmetric Property of Equality. & g. x=15 & g. Symmetric Property of Equality

Completed Proof

Finally, we can view the completed proof table.

Statements	Reasons
a. 1/5x+3=2x-24	a. Given
b. 5(1/5x+3)=5(2x-24)	b. Multiplication Property of Equality
c. x+15=10x-120	c. Distributive Property
d. 15=9x-120	d. Subtraction Property of Equality
e. 135=9x	e. Addition Property of Equality
f. 15=x	f. Division Property of Equality
g. x=15	g. Symmetric Property