Question

the following inequality has a solution in the form \\(x \le a\\). solve the inequality and place the correct value of \\(a\\) into the box.

\\2(x - 8) + 4 \le -5x - 4\\

answer: \\(x \le\\)

enter your answer as an integer or a reduced fraction in the form a/b.

question help: video

Explanation:

Expand the left side of the inequality

Using the Solving Inequalities knowledge point

$$ 2(x - 8) + 4 \le -5x - 4 \implies 2x - 16 + 4 \le -5x - 4 $$

Simplify the constant terms on the left side

Using the Solving Inequalities knowledge point

$$ 2x - 12 \le -5x - 4 $$

Isolate the variable terms on one side

Using the Solving Inequalities knowledge point

$$ 2x + 5x \le -4 + 12 \implies 7x \le 8 $$

Solve for x

Using the Solving Inequalities knowledge point

$$ x \le \frac{8}{3} $$

Answer:

The following inequality has a solution in the form \(x \le A\). Solve the inequality and place the correct value of \(A\) into the box.

\(2(x - 8) + 4 \le -5x - 4\)

Answer: \(x \le\) <blank>\(\frac{8}{3}\)</blank>

Enter your answer as an integer or a reduced fraction in the form A/B.