Question

Solve the system of inequalities: \(6-4a \geq 2\) and \(3a-1 < 8\).

(A) True
(B) False

Answer 1

To solve the system of inequalities, 6-4a ≥ 2 and 3a-1 < 8, we first solve each inequality separately and then find the intersection of the solutions to get that the solution is a ≤ 1.

Step-by-step explanation:

To solve the system of inequalities 6-4a ≥ 2 and 3a-1 < 8, begin by isolating the variable a in each inequality.

For the first inequality, subtract 6 from both sides:

-4a ≥ 2 - 6

-4a ≥ -4

Divide both sides by -4 (remember to reverse the inequality):

a ≤ 1

For the second inequality, add 1 to both sides:

3a < 8 + 1

3a < 9

Divide both sides by 3:

a < 3

Now, you have a ≤ 1 and a < 3. Since a < 3 includes values less than 1, the solution to the system is a ≤ 1.