Question

Solve the inequality (7(x-5) < 2(4x - 1)) and write the solution set in interval notation.

a.(-[infinity], -3)
b.(-[infinity], 5)
c.(5, [infinity])
d. ∅

Answer 1

To solve the inequality (7(x-5) < 2(4x - 1)), distribute and combine like terms. Then, isolate the variable x by dividing both sides by -1 and flipping the inequality sign. The solution set is (-33, ∞).

Step-by-step explanation:

To solve the inequality (7(x-5) < 2(4x - 1)), distribute and combine like terms. Then, isolate the variable x by dividing both sides by -1 and flipping the inequality sign.

First, distribute the coefficients:

• 7x - 35 < 8x - 2

Next, combine like terms:

• 7x - 8x < -2 + 35

-x < 33

Now, divide both sides by -1, remembering to flip the inequality sign:

• x > -33

The solution set, written in interval notation, is (-33, ∞).