Question

Mathematical Statement Justification

4x + 3 = x + 5 − 2x Given

4x + 3 = x − 2x + 5 Commutative Property of Addition

4x + 3 = −x + 5

5x + 3 = 5

5x = 2

x = two fifths

Fill in the missing justifications in the correct order.

A. Combine Like Terms; Subtraction Property of Equality; Addition Property of Equality; Division Property of Equality

B. Combine Like Terms; Addition Property of Equality; Subtraction Property of Equality; Division Property of Equality

C. Addition Property of Equality; Combine Like Terms; Subtraction Property of Equality; Division Property of Equality

D. Subtraction Property of Equality; Division Property of Equality; Addition Property of Equality; Combine Like Terms

Answer 1

B. Combine Like Terms; Addition Property of Equality; Subtraction Property of Equality; Division Property of Equality

Explanation:

I took the quiz and got it right

Answer 2

B

Explanation:

1. Given mathematical statement

`4x+3=x+5-2x`

So,

`\begin{array}{cc}4x+3=x+5-2x&\text{ Given}\end{array}`

2. Rewrite it as

`4x+3=x-2x+5`

So,

`\begin{array}{cc}4x+3=x-2x+5&\text{ Commutative property of addition}\end{array}`

3. Combine like terms
`x` and
`-2x:`

`4x+3=-x+5`

So,

`\begin{array}{cc}4x+3=-x+5&\text{ Combine like terms}\end{array}`

4. Add
`x` to both sides:

`4x+3+x=-x+5+x\\ \\5x+3=5`

So,

`\begin{array}{cc}5x+3=5&\text{ Addition property of equality}\end{array}`

5. Subtract 3 from both sides:

`5x+3-3=5-3\\ \\5x=2`

So,

`\begin{array}{cc}5x=2&\text{ Subtraction property of equality}\end{array}`

6. Divide both sides by 5:

`x=(2)/(5)`

So,

`\begin{array}{cc}x=(2)/(5)&\text{ Division property of equality}\end{array}`