4 − (x + 2) < −3(x + 4)

x<-7

Step-by-step explanation:

4 − (x + 2) < −3(x + 4)

4 − x - 2< −3x - 12

14 < - 2x

x<-7

Answer and Step-by-step explanation:

First, we need to solve both sides of the equation.

Distribute the negative to the x and the 2.

4 - x - 2 < -3(x + 4)

Distribute the -3 to the x and the 4.

4 - x - 2 < -3x - 12

Combine like terms.

2 - x < -3x - 12

Add 12 to both sides of the equation.

12 + 2 - x < -3x - 12 + 12

14 - x < -3x

Add x to both sides of the equation.

14 - x + x < -3x + x

14 < -2x

*Divide both sides of the equation by -2, and flip the sign.

-7 > x

-7 > x is the answer.

*How this works:

When we flip the sign, we really are just saving ourselves an extra step when dividing numbers (that are negative, only works when number is negative).

14 < -2x

If we were to add to x, and subtract 14, it will look like this:

2x < -14

Then when we divide by 2, we get:

x < -7

This is the same result, but it takes an extra step. Use this way if you forget why you need to flip the sign when dividing by a negative number.

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I hope this helps!

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step-by-step explanation: