McGraw Hill Integrated II, 2012
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McGraw Hill Integrated II, 2012 View details
2. Algebraic Proof
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Exercise 17 Page 288

Solve the equation to determine the steps involved. Then choose the Properties of Equality.

Statements
Reasons
a. 8-3x/4=32
a. Given
b. 4(8-3x/4)=4(32)
b. Multiplication Property of Equality
c. 8-3x=128
c. Substitution Property of Equality
d. - 3x=120
d. Subtraction Property of Equality
e. x=- 40
e. Division Property of Equality
Practice makes perfect

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

  • Given: 8-3x/4=32
  • Prove: x=- 40

In order to complete the table, and prove that x=- 40, we will solve the equation.

Blank b

Let's start!
8-3x/4=32
4(8-3x/4)= 4(32)

We began by multiplying both sides of the equation by 4, which can be justified by the Multiplication Property of Equality. & b. 4(8-3x/4)=4(32) & b. Multiplication Property of Equality

Blank c

We will continue with the next step of the proof.
4(8-3x/4)=4(32)
8-3x=128
Here, we multiplied. This means that we are substituting equivalent values. For instance, because 4(32) = 128, we can replace 4(32) with 128. Therefore, the property that justifies this step is the Substitution Property of Equality. & c. 8-3x=128 & c. Substitution Property of Equality

Blank d

Let's continue solving the equation.
8-3x=128
8-3x- 8=128- 8
- 3x=120
We subtracted 8 from both sides of the equation and simplified the obtained equation. Therefore, the property that justifies this step is the Subtraction Property of Equality. & d. - 3x=120 & d. Subtraction Property of Equality

Blank e

Next, we will fill in the last blank.
- 3x=120
- 3x/-3=120/-3
x=-40
By dividing each side of the equation by -3, we found the value of x. The property that justifies this step is the Division Property of Equality. & e. x=-40 & e. Division Property of Equality

Completed Proof

Finally, we can view the completed proof table.

Statements
Reasons
a. 8-3x/4=32
a. Given
b. 4(8-3x/4)=4(32)
b. Multiplication Property of Equality
c. 8-3x=128
c. Substitution Property of Equality
d. - 3x=120
d. Subtraction Property of Equality
e. x=- 40
e. Division Property of Equality