Question

What is `3 |x + 4| = 10` ?

`3 |x + 4| = 10`

Answer 1

`x=+-10/3-4~~-7.33 or -0.667`

Explanation:

`3|x+4|=10`

Divide both sides by `3`,

`|x+4|=10/3`

Remove modulus,

`x+4=+-10/3`

Solve,

`x=+-10/3-4~~-7.3333 or -0.66666`

Answer 2

`x = -2/3`

`x = -22/3`

Explanation:

Since we have an absolute value, we must split the equation in the two possible scenarios:

Scenario 1: `x+4>0`

This means that `x> -4` and `|x+4|=x+4`. The equation becomes

`3(x+4)=10`
`therefore 3x+12=10`
`therefore 3x = -2`
`therefore x = -2/3`

This is compatible with the condition `x> -4`, so we accept the solution.

Scenario 2: `x+4<0`

This means that `x< -4` and `|x+4|=-x-4`. The equation becomes

`-3(x+4)=10`
`therefore -3x-12=10`
`therefore -3x = 22`
`therefore x = -22/3`

This is compatible with the condition `x< -4`, so we accept the solution.