Question

How do you solve `8/(x+2)+8/2=5`?

Answer 1

`x = 6`

Explanation:

Given: `8/(x+2) + 8/2 = 5`

One way to solve is by realizing that `8/2 = 4`, so substitute this value into the equation: `" "8/(x+2) + 4 = 5`

Simplify by subtracting `4` from both sides of the equation:
`8/(x+2) + 4 - 4= 5 - 4`;

`8/(x+2)= 1`

Multiply both sides of the equation by `x+2`:

`cancel(x+2) * 8/(cancel(x+2)) = 1 * (x + 2)`

Simplify: `" "8 = x + 2`

Subtract both sides of the equation by `2`:

`8 - 2 = x + 2 - 2`

`6 = x`

A second way to solve is by finding a common denominator for both sides of the equation `2(x+2)`:

`8/(x+2) * 2/2 + 8/2 * (x+2)/(x+2) = 5 *(2(x+2))/(2(x+2))`

Simplify:

`(16 +8(x+2))/(2(x+2)) = (10(x+2))/(2(x+2))`

Since both denominators are equal, we can set the numerators equal to solve:

`16 +8(x+2) = 10(x+2)`

Distribute:

`16 + 8x + 16 = 10x + 20`

Add like terms on the same side:

`32 + 8x = 10x + 20`

Subtract `20` from both sides:

`32 - 20 + 8x = 10x + 20 - 20`

`12 + 8x = 10x`

Subtract `8x` from both sides: `" "12 + 8x - 8x = 10x - 8x`

Simplify: `" "12 = 2x`

Divide both sides by `2: " "12/2 = (2x)/2`

Simplify: `" "6 = x`