Question

State all integer values of a in the interval [-5, 2] that satisfy the following inequality: 3x+1>-9

Answer 1

The answer is that the integer values of "a" in the interval [-5, 2] that satisfy the inequality 3x + 1 > -9 are -5, -4, -3, -2, -1, 0, 1, and 2.

Explanation:

To find the integer values of "a" in the interval [-5, 2] that satisfy the inequality 3x + 1 > -9, let's solve it step by step.

Step 1: Subtract 1 from both sides of the inequality:

3x > -10

Step 2: Divide both sides of the inequality by 3:

x > -10/3

Step 3: Evaluate the integer values of "a" in the interval [-5, 2] that are greater than -10/3:

For -5: -5 > -10/3 - True

For -4: -4 > -10/3 - True

For -3: -3 > -10/3 - True

For -2: -2 > -10/3 - True

For -1: -1 > -10/3 - True

For 0: 0 > -10/3 - True

For 1: 1 > -10/3 - True

For 2: 2 > -10/3 - True

Step 4: Identify the values of "a" that satisfy the inequality in the given interval:

The integer values of "a" in the interval [-5, 2] that satisfy the inequality 3x + 1 > -9 are -5, -4, -3, -2, -1, 0, 1, and 2.