Question

complete the proof: given: 10 - 2x = 3(x - 2) + 4 prove: x = 12/5 1. 10 - 2x = 3x - 6 + 4 2. 10 - 2x = 3x - 2 3. 10 = 5x - 2 4. 12 = 5x 5. 12/5 = x 6. x = 12/5 choose your answer... distribution combine like terms addition property of equality(1) addition property of equality(2) division property of equality

Explanation:

Step1: Apply Distribution

$10 - 2x = 3x - 6 + 4$ (Expand $3(x-2)$ to $3x - 6$)

Step2: Combine like terms

$10 - 2x = 3x - 2$ (Simplify $-6 + 4 = -2$)

Step3: Use Addition Property of Equality (1)

$10 = 5x - 2$ (Add $2x$ to both sides)

Step4: Use Addition Property of Equality (2)

$12 = 5x$ (Add $2$ to both sides)

Step5: Use Division Property of Equality

$\frac{12}{5} = x$ (Divide both sides by $5$)

Step6: Rewrite equation

$x = \frac{12}{5}$ (Symmetric property of equality)

Answer:

1. Distribution, 2. Combine like terms, 3. Addition Property of Equality (1), 4. Addition Property of Equality (2), 5. Division Property of Equality, 6. (Rewriting, not listed in options)