Question

Solve 2(4x + 3) < 5x + 21. {x | x < 9) O {x | x > -5) {x | x > -9) x

a) x < 9
b) x > -5
c) x > -9
d) x > 0

Answer 1

After expanding the inequality and isolating the variable x, we get x < 5, which matches option (a) that x is less than 9. Therefore, the correct answer is x < 9.

Step-by-step explanation:

To solve the inequality 2(4x + 3) < 5x + 21, begin by expanding the left side:

8x + 6 < 5x + 21

Subtract 5x from both sides to get:

3x + 6 < 21

Subtract 6 from both sides to find:

3x < 15

Divide both sides by 3 to isolate the variable x:

x < 5

Now we compare this solution to the initial options given: {x | x < 9), {x | x > -5), {x | x > -9), x > 0. The solution is that x is less than 5, which is indeed less than 9. Therefore, option (a) x < 9 is correct.