Question

-33>-4x-5 or -4x-5≥-49.Solve for x and graph the solution on the number line below

Answer 1

Answer: 7 < x or x ≤ 11. See attached for the graph.

Explanation:

We will solve each inequality for x.

Given:

-33 > -4x - 5

Add 5 to both sides of the inequality:

-28 > -4x

Divide both sides of the equation by -4:

➜ When dividing/multiplying by a negative, flip the direction of the sign.

7 < x

Again, we will solve for x.

Given:

-4x - 5 ≥ -49

Add five to both sides of the inequality:

-4x ≥ -44

Divide both sides of the inequality by -4:

➜ When dividing/multiplying by a negative, flip the direction of the sign.

x ≤ 11

Lastly, we can graph both of these inequalities. We use an open circle for "<" at 7 and a closed circle for "≤" at 11. These graphs are below.

Answer 2

A graph of each linear inequality is shown on the number line in the pictures below.

In Mathematics, an inequality is a relation that compares two or more numerical data and variables in an algebraic equation based on any of the following inequality symbols:

• Less than or equal to (≤).
• Greater than (>).
• Greater than or equal to (≥).
• Less than (<).

Based on the information provided, we can logically deduce that solution set is given by;

-33 > -4x - 5

4x > 33 - 5

4x > 28

x > 28/4

x > 7

-4x - 5 ≥ -49

49 - 5 ≥ 4x

4x ≤ 49 - 5

4x ≤ 44

x ≤ 44/4

x ≤ 11