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!