Question

question 18

what is the solution set for the following inequality?

(2x - 6 < 4(1 + x))

• (x < 5)
• (x < -5)
• (x > 5)
• (x > -5)

Explanation:

Expand the right side

Using the Linear Inequalities knowledge point

$$ 2x - 6 < 4(1 + x) \implies 2x - 6 < 4 + 4x $$

Isolate the variable terms

Using the Linear Inequalities knowledge point

$$ 2x - 4x < 4 + 6 \implies -2x < 10 $$

Solve for x

Using the Inequality Sign Reversal knowledge point

$$ x > \frac{10}{-2} \implies x > -5 $$

Answer:

• \(x < 5\)
• \(x < -5\)
• \(x > 5\)
• \(x > -5\) (Correct answer)