olve for x and graph the solution on the number line below.

Question

58≥5x+3>
−42

Answer 1

To solve for x, we need to isolate x in the inequality.

Starting with 58 ≥ 5x + 3, we subtract 3 from both sides:

58 - 3 ≥ 5x

55 ≥ 5x

Now, divide both sides by 5:

55/5 ≥ x

11 ≥ x

So, x ≤ 11.

Next, we have the inequality -42:

-42 ≤ 5x + 3

Subtract 3 from both sides:

-42 - 3 ≤ 5x

-45 ≤ 5x

Divide both sides by 5 (keeping in mind the sign change for dividing by a negative number):

-45/5 ≥ x

-9 ≥ x

So, x ≤ -9.

Combining the two solutions, we have:

x ≤ -9 or x ≤ 11.

Graphically, this can be represented on the number line as follows:

<------[------------][-------)------>

-9 11