Inequalities

Question

On my math paper I had the following equation:

 

5/4(x+4) ≤ ½(x+8) -8

 

This is my work:

 

5/4(x+4) ≤ ½(x+8) -8

4(5/4(x+4) ≤ ½(x+8) -8)

5(x+4) ≤ 2(x+8) -32

5x+20 ≤ 2x+16-32

-2x        -2x

3x+20 ≤ -16

    -20     -20

3x ≤ -36

—————

      3

x= -12

 

Check:

5/6(-12+4) ≤ ½ (-12 +8) -8

5/6 (-8) ≤ ½ (-4) -8

-40/6 ≤ (-2) -8

-40/6 ≤ 16

 

 

I was wondering if my work was correct... The  answer checks alright but I feel like it's not right. Please help before Thursday! 

Answer 1

Your work is correct (just change your equal sign in your answer to a less than or equal to sign)...however, you need to double-check your "check".

 

You have started the problem with the wrong fraction (it should be 5/4 instead of 5/6). Also, the right side is not (-2) times (-8). It is -2 minus 8, resulting in -10.

 

With those changes in place, you will have -10 is less than or equal to -10 which is correct : ) 

 

 

Answer 2

Very very close. Your work is all correct, but remember your inequalities sign. You started with ≤ instead of =, so your answer should reflect that, too.

Instead of x = -12, it needs to be x ≤ -12