Question

grade math homework
name
class:
1/22/2026

1. which of these expressions is equivalent to 3(x - 2)?

a. 3x - 6
b. 3x - 2
c. 3x + 2
d. 3x + 6

1. which of these expressions is equivalent to -2(x - 5)?

a. -2x - 5
b. -2x + 5
c. -2x + 10
d. -2x - 10

Explanation:

Question 1

Step1: Apply distributive property

The distributive property states that \(a(b - c)=ab - ac\). For \(3(x - 2)\), we distribute 3 to both \(x\) and \(-2\).
\[3(x - 2)=3\times x-3\times2\]

Step2: Simplify the terms

Calculate \(3\times x = 3x\) and \(3\times2 = 6\), so the expression becomes:
\[3x - 6\]

Step1: Apply distributive property

The distributive property is \(a(b - c)=ab - ac\). For \(-2(x - 5)\), we distribute \(-2\) to both \(x\) and \(-5\).
\[-2(x - 5)=-2\times x-(-2)\times5\]

Step2: Simplify the terms

Calculate \(-2\times x=-2x\) and \(-(-2)\times5 = 10\) (because multiplying two negative numbers gives a positive), so the expression becomes:
\[-2x + 10\]

Answer:

A. \(3x - 6\)

Question 2