Question

Solve: `(x + 1)/(2x + 3) = 3/8`.

Answer 1

`(x + 1)/(2x + 3) = 3/8`.

We multiply both sides of the equation by (2x + 3),

`((x + 1)/(2x + 3)) xx (2x + 3) = 3/8 xx (2x + 3)`

(2x + 3) gets cancelled on the LHS we have then,

`x + 1 = (3(2x + 3))/8`

Multiplying both sides by 8,

8(x + 1) = 3(2x + 3)

or 8x + 8 = 6x + 9

or 8x = 6x + 9 - 8

or 8x = 6x + 1

or 8x - 6x = 1

or 2x = 1

or x = `1/2`

The solution is x = `1/2`.

Check:

Number of LHS = `1/2 + 1 = (1 + 2)/2 = 3/2`

Denominator of LHS = 2x + 3 = 2 × `1/2` + 3 = 1 + 3 = 4.

LHS = numerator ÷ denominator = `3/2 ÷ 4 = 3/2 xx 1/4 = 3/8.`

LHS = RHS.