determine the largest integer value of a when x=-1

Question

given 2x+ax-7>-12, determine the largest integer value of a when x=-1

Answer 1

2x+ax-7>-12

 

Rearrange the terms so that the x's are on the left and the constants are on the right.

To do this, add 7 to both sides.

 

2x + ax > -5

When x = -1

2(-1) + a(-1) >-5

-2-a>-5

 

Add 2 to both sides to get

-a>-3

Now divide by -1 and remember that when multiplying or dividing an inequality by a negative number the inequality changes.  

So a<3.  Notice the > changed to <

 

Since this is a strict inequality, a cannot = 3, so the largest integer value of a is 2, when x = -1