Question

Solve for x.


1/2 ( 3/5x − 1/2) > x +3/8

Answer 1

`(1)/(2) ((3)/(5) x-(1)/(2) ) > x+(3)/(8)`

Simplify:

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

Subtract x from both sides:

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

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

Add
`(1)/(4)` to both sides:

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

`-(7)/(10) x > (5)/(8)`

Multiply both sides by
`-(10)/(7)`:

`(-(10)/(7) )*(-(7)/(10) x) > (-(10)/(7) )*((5)/(8) )`

Since we are multiplying inequalities by negative numbers, the sign will reverse.

`\fbox{x} < \fbox{-$(25)/(28) $}`

Answer 2

`x < - (25)/(28)`

Explanation:

Given inequality:

`(1)/(2)\left((3)/(5)x-(1)/(2)\right) > x+(3)/(8)`

Distribute:

`\implies (1)/(2)\cdot (3)/(5)x- (1)/(2)\cdot (1)/(2) > x+(3)/(8)`

`\implies (3)/(10)x- (1)/(4) > x+(3)/(8)`

Add 1/4 to both sides:

`\implies (3)/(10)x- (1)/(4) +(1)/(4) > x+(3)/(8)+(1)/(4)`

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

Subtract x from both sides:

`\implies (3)/(10)x-x > x+(3)/(8)+(1)/(4)-x`

`\implies (3)/(10)x-x > (3)/(8)+(1)/(4)`

Rewrite fractions so that the denominators are the same on each side fo the inequality:

`\implies (3)/(10)x-(10)/(10)x > (3)/(8)+(2)/(8)`

`\implies-(7)/(10)x > (5)/(8)`

Multiply both sides by 10/7:

`\implies-(7)/(10)x \cdot (10)/(7) > (5)/(8)\cdot (10)/(7)`

`\implies-x > (50)/(56)`

`\implies-x > (25)/(28)`

Divide both sides by -1 (remembering to reverse the inequality sign):

`\implies x < - (25)/(28)`