Question

Consider the inequalities -1/4a>3 and b-12>-3. What values, if any, makeboth inequalities true? Show your work.

Answer 1

To solve the inequalities -1/4a > 3 and b - 12 > -3, a must be less than -12, and b must be greater than 9. By solving each inequality, we determine the sets of valid values for a and b that satisfy both inequalities at the same time.

Step-by-step explanation:

To solve the inequalities -1/4a > 3 and b - 12 > -3, we must isolate the variables a and b on one side of each inequality.

1. Multiply both sides of the first inequality by -4 to get a < -12. Remember to reverse the inequality sign when you multiply or divide by a negative number.
2. Add 12 to both sides of the second inequality to get b > 9.

The solutions to the inequalities are the sets of all a such that a < -12 and all b such that b > 9. These sets of values for a and b make both inequalities true.

Answer 2

The given inequalities are

- a/4 > 3

b - 12 > - 3

For the first inequality,

- a/4 > 3

- a > 4 x 3

- a > 12

If we divide both sides of the inequality by - 1, the symbol reverses. thus, we have

a < - 12

For the esecond inequality,

b - 12 > - 3

b > - 3 + 12

b > 9

The values of a are all numbers less than - 12

The values of b are all numbers greater than 9

there is no value that it common to these sets of numbers. Thus, no value makes both inequalities true