Final answer:
The inequality −4≤5x−4≤21 is solved by first adding 4 to each part, then dividing by 5 to get 0 ≤ x ≤ 5, which means the correct answer is option a) x≤5.
Step-by-step explanation:
To solve the inequality −4≤5x−4≤21, we must isolate the variable x. We can do this by performing the same operations to each part of the compound inequality. Begin by adding 4 to each part:
−4 + 4 ≤ 5x − 4 + 4 ≤ 21 + 4
0 ≤ 5x ≤ 25
Now, we divide each part of the inequality by 5 to solve for x:
0 ÷ 5 ≤ 5x ÷ 5 ≤ 25 ÷ 5
0 ≤ x ≤ 5
The solution to the inequality is x is less than or equal to 5, which is option a) x≤5.