Question

How do you solve `\frac { 3} { 4} ( x + 8) > \frac { 1} { 2} ( 2x + 10)`?

Answer 1

`x < 4`

Explanation:

Since one denominator is 4 and the other is 2, multiply both sides by `4` to get rid of both denominators:

`3/4(x+8) > 1/2(2x+10)`

`4*3/4(x+8) > 4*1/2(2x+10)`

`color(white)"-" 3(x+8) > 2(2x+10)`

Now, distribute the `3` and `2`, respectively.

`color(white)"-" 3*x + 3*8 > 2*2x + 2*10`

`color(white)"-." 3x + 24 > 4x + 20`

Subtract `3x` from both sides.

`color(white)"-.."3x+24 - 3x > 4x + 20 - 3x`

`24 > x + 20`

Finally, subtract `20` from both sides.

`color(white)"-" 24 - 20 > x + 20 - 20`

`color(white)"-" 4 > x`

Flip the inequality so `x` is on the left (this is optional but recommended). Remember to flip the sign as well!

`color(white)"-" x < 4`

Final Answer