Question

Solve each absolute value inequality and show its solution set. l) −2x−5 ≤5

Answer 1

To solve the inequality −2x−5 ≤ 5, we add 5 to both sides and then divide by −2, flipping the inequality to get x ≥ −5. The solution set is all numbers greater than or equal to negative five.

Step-by-step explanation:

To solve the absolute value inequality −2x−5 ≤ 5, we first isolate the absolute value expression.

The inequality does not involve an absolute value directly but can be compared to one. The objective is to find the values of x that satisfy this inequality.

The steps to solve the inequality are as follows:

Add 5 to both sides of the inequality to get −2x ≤ 10.

Divide both sides by −2 to get x ≥ −5. Remember that dividing by a negative number flips the inequality sign.

The solution set for the inequality is x ≥ −5. This means that any number greater than or equal to negative five will satisfy the inequality.

Answer 2

To solve this inequality, we must first isolate the absolute value on one side of the equation.

Step 1: Add 5 to both sides of the equation.

−2x−5 + 5 ≤ 5 + 5

Step 2: Simplify the left side.

−2x ≤ 10

Step 3: Divide both sides by -2.

x ≥ -5

Step 4: Graph the solution on a number line.

The solution set is x ≥ -5