How do i solve an inequality like this 4x-5>7-8x?

Same as an equality: Treat both sides the same. The only difference is when you multiply or divide both sides by a negative number, the direction of the > changes to <. But, that doesn't occur here.

Add 8x to both sides
4x - 5 > 7 - 8x
12x - 5 > 7

Add 5 to both sides
12x > 12

Divide both sides by 12
x > 1

4x - 5 > 7 - 8x
4x + 8x > 7 + 5
12x > 12
x > 1

Answer: x > 1

4x - 5 > 7 - 8x
4x + 8x > 7 + 5
12x > 12
x > 12/12
x > 1

12 x > 12

x > 1

4x-5>7-8x

4x + 8x>7 +5

12 x > 12

x > 1




QED

You put the x variables on one side, and the numbers on the other side, and solve as if it's a normal equation... but instead of =, you have >.

4x+8x>7+5
12x>12
by dividing both sides by 12, to have the coefficient of x to be one,
x>1