Question

Solve the inequality 30 ≥ 6(2/3z + 1/3).

Solve the inequality 15.6 < 2.7(z-1)-0.6.

Are there any values of z that solve both inequalities? Use a number line to support your answer.

Answer 1

The solution set of the inequality is z ≤ 7 and z < 7

No, there are no values of z that solve both inequalities

How to determine the solution to the inequality

Inequality 1

First, distribute the 6 on the right side of the inequality:

30 ≥ 4z + 2

Then, subtract 2 from both sides:

28 ≥ 4z

Divide both sides by 4:

7 ≥ z

So the solution set of the inequality is z ≤ 7.

Inequality 2

First, distribute the 2.7 on the right side of the inequality:

15.6 < 2.7z - 2.7 - 0.6

Then, add 2.7 and 0.6 on both sides:

18.9 < 2.7z

Divide both sides by 2.7:

z > 7

So the solution set of the inequality is z > 7

Do they have common z values

The inequality z ≤ 7 states that z is less than or equal to 7. This means that any value of z that is less than or equal to 7 will satisfy the inequality.

The inequality z > 7 states that z is greater than 7. This means that any value of z that is greater than 7 will satisfy the inequality.

Since, they have different values that satisfy them, thus, there are no values of z that will solve both of them.

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