Question

which two expressions are equivalent to 6(x + 5) - 4(x + 5)?
a 2(x + 5)
b 2x + 10
c 2x + 5
d 2(3x + 5)

Explanation:

Step1: Simplify the given expression

First, we expand the expression \(6(x + 5)-4(x + 5)\) using the distributive property \(a(b + c)=ab+ac\).
For \(6(x + 5)\), we get \(6x+30\), and for \(-4(x + 5)\), we get \(-4x - 20\).
So the expression becomes \(6x + 30-4x - 20\).

Step2: Combine like terms

Combine the \(x\)-terms: \(6x-4x = 2x\).
Combine the constant terms: \(30 - 20=10\).
So the simplified expression is \(2x + 10\).

Now let's check the options (assuming the options are: A. \(2x + 10\), B. \(2x+25\), C. \(2x + 5\), D. \(3x + 10\)):

• Option A: \(2x + 10\) matches our simplified result.
• Option B: \(2x+25\) does not match.
• Option C: \(2x + 5\) does not match.
• Option D: \(3x + 10\) does not match.

Answer:

A. \(2x + 10\)