Question

Solve for x in 4−(x+2)<−3(x+4)

A.0B.x>−9
C.x>−7
D.x<−9

Answer 1

To solve 4−(x+2)<−3(x+4), distribute the negative signs, combine like terms, and solve for x to find that x < -7.

Step-by-step explanation:

The question requires solving the inequality 4−(x+2)<−3(x+4). To solve this, we'll perform the following steps:

1. Distribute the negative sign on the left and distribute -3 on the right to get rid of the parentheses.
2. Combine like terms on both sides of the inequality.
3. Isolate the variable on one side to solve for x.

Performing these steps, the solution is:

1. 4 - x - 2 < -3x - 12
2. 2 - x < -3x - 12 (after combining 4 and -2)
3. 2 + 3x < -12 + x (adding 3x and subtracting x from both sides)
4. 2 + 2x < -12 (combining like terms)
5. 2x < -14 (subtracting 2 from both sides)
6. x < -7 (dividing both sides by 2)

Thus, the solution to the inequality 4−(x+2)<−3(x+4) is x < -7, which matches option C.