Find the value of x for \(\frac{2 + 2x}{3} - 2 \geq \frac{4x - 6}{5}\)
A
x \(\geq\) -5
B
x \(\geq\) -1
C
x \(\leq\) -1
D
x \(\leq\) 3
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
\(\frac{2 + 2x}{3} - 2 \geq \frac{4x - 6}{5}\)
\(\frac{2 + 2x - 6}{3} \geq \frac{4x - 6}{5}\)
\(\frac{2x - 4}{3} \geq \frac{4x - 6}{5}\)
\(5(2x - 4) \geq 3(4x - 6)\)
\(10x - 20 \geq 12x - 18\)
\(10x - 12x \geq -18 + 20\)
\(-2x \geq 2\)
\(x \leq -1\)
Source: Myschool Past Questions Archive (Record #55394)