Question

Determine the smallest integer value of x in the solution of the following inequality: -5x-6 ≤ 17.

Answer 1

To find the smallest integer value of x that satisfies the inequality -5x-6 ≤ 17, add 6 to both sides, divide by -5, and round the result up to the nearest integer. The answer is x ≥ -4.

Step-by-step explanation:

To determine the smallest integer value of x in the solution of the inequality -5x-6 ≤ 17, follow these steps:

1. Add 6 to both sides of the inequality: -5x - 6 + 6 ≤ 17 + 6, which simplifies to -5x ≤ 23.
2. Divide both sides by -5, remembering that dividing by a negative number reverses the inequality sign: -5x / -5 ≥ 23 / -5, which simplifies to x ≥ -4.6.
3. Since we are looking for the smallest integer value of x, we round -4.6 up to the nearest integer, which is -4, because it is the smallest integer greater than or equal to -4.6.

The smallest integer value of x that satisfies the inequality is -4.