Question

Solve for x.

−ax + 2b > 8
x < the quantity negative 2 times b plus 8 all over negative a
x > the quantity negative 2 times b plus 8 all over negative a
x < the quantity 2 times b minus 8 all over negative a
x > the quantity negative 2 times b minus 8 all over a

Answer 1

Remark

Why don't we just solve the expression, and then see which one of the answers fit.

Step One.

You are eventually going to divide by - a. On of the most confusing problems with inequality equations is what to do about a - division. The answer is (in this case) to add ax to both sides of the equation.

-ax + ax + 2b > 8 + ax

2b > 8 + ax

Step two

Solve for x. Subtract 8 from both sides.

2b - 8 > 8 - 8 + ax

2b - 8 > ax

Step 3

Divide by a

(2b - 8)/a > x

Step Four

Find the answer.

I'm getting none of the answers above.

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My answer is actually correct. The question now goes through the convoluted process of multiplying top and bottom of the answer by -1. Why I don't know. I suppose just so you can get an answer that is given.

If you do that, you get

(8 - 2b)/-a > x which is the first answer, I think.

Answer 2

Begin by subtracting 2b from both sides. This will give us

-ax > -2b +8

Then we will divide by -a. This division by a negative number changes the direction of the inequality sign. When we divide by -a:

`x<(-2b+8)/(-a)`