Question

Which inequality is equivalent to the given inequality? -4(x+7)<3(x-2)

A. -7x<22
B. -7x>-34
C. -7x<-34
D. -7x>22

Answer 1

To find the equivalent inequality, we distribute the numbers, combine like terms, and isolate the variable x, ending up with the inequality -7x < 22, which corresponds to option A.

Step-by-step explanation:

The question asks to find an equivalent inequality to the inequality -4(x+7)<3(x-2). Let's first simplify the inequality:

1. Distribute the -4 and 3 on each side: -4x - 28 < 3x - 6.
2. Next, add 4x to both sides to get the x terms on one side: -28 < 7x - 6.
3. Now, add 6 to both sides: -22 < 7x, which after flipping the inequality for clarity becomes 7x > -22.
4. Finally, we can divide by 7 to isolate the variable x, which gives us x > -22/7. However, we need to keep the x on the left side to match the answer choices, so we multiply both sides by -1 and change the direction of the inequality to maintain the correct relationship, resulting in -7x < 22.

Therefore, the inequality that is equivalent to the given inequality is -7x < 22, which corresponds to option A. -7x < 22.