Question

Solve each of the following inequalities for the given variable. Represent

your solutions on a number line.
a. 2(3p + 1) > -4
b. 9k-2 <3k + 10
c. 5-h24

Answer 1

To solve the provided inequalities, distribute and simplify, combine like terms, isolate the variable, and represent the solutions on a number line.

Step-by-step explanation:

To solve each of the given inequalities, we will follow these steps:

1. Distribute and simplify, if necessary.
2. Combine like terms, if possible.
3. Isolate the variable on one side of the inequality.
4. Divide or multiply by a positive number, if needed.
5. Represent the solutions on a number line.

a. For the inequality 2(3p + 1) > -4:

First, distribute and simplify: 6p + 2 > -4. Then, subtract 2 from both sides to isolate the variable: 6p > -6. Divide by 6 to solve for p: p > -1.

b. For the inequality 9k - 2 < 3k + 10:

First, combine like terms: 6k - 2 < 10. Next, add 2 to both sides to isolate the variable: 6k < 12. Divide by 6 to solve for k: k < 2.

c. It seems there is an error in the third inequality as it is not in the form of an inequality. Please provide the correct inequality to solve for h.