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

Answer:

B

Step-by-step 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:

$x=\dfrac{2}{5}$

So,

$\begin{array}{cc}x=\dfrac{2}{5}&\text{ Division property of equality}\end{array}$

Answer 2

Answer:

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

Step-by-step explanation:

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