Question

I will attach the problem.

Answer 1

Deal with each side individually.

~~~~~ LEFT HAND SIDE ~~~~~

\[−4 ≤ −2x+6\]\[−4−6 ≤ −2x\]\[−10 ≤ −2x\]

Swap the two sides over so we dont have to deal with negatives
\[2x ≤ −10\]\[x ≤ 5\]

~~~~~ RIGHT HAND SIDE ~~~~~
\[-2x+6 ≤ 13\]\[-2x ≤ 13 - 6\]\[-2x ≤ 7\]\[-7 ≤ 2x\]\[-4.5 ≤ x\]

Put the two halves back together to get:

\[-4.5 ≤ x ≤ 5\]

Answer 2

Thanks for good illustration, davejavous

Answer 3

You can keep it all in one complex inequality:

\(-4 \le -2x + 6 \le 13\)

Subtract 6 from all three sides:

\(-10 \le -2x \le 7\)

Divide all three sides by -2.
Remember that when you multiply or divide an inequality by a negative number, the inequality sign changes direction.

\(5 \ge x \ge -\dfrac{7}{2}\)

Rewrite the inequality with the smaller number first:

\(-\dfrac{7}{2} \le x \le 5\)

or

\(-3.5 \le x \le 5\)


Notice that \(\dfrac{7}{2} = 3.5\), not 4.5