Question

Solve the equation below for b: |3b+4|=11

Answer 1

b = - 5 , b =
`(7)/(3)`

Explanation:

given

| 3b + 4 | = 11

The absolute value function always gives a positive value

However, the expression inside can be positive or negative

There are then 2 equations to solve

3b + 4 = 11 ( subtract 4 from both sides )

3b = 7 ( divide both sides by 3 )

b =
`(7)/(3)`

And

- (3b + 4) = 11 ← distribute parenthesis on left side )

- 3b - 4 = 11 ( add 4 to both sides )

- 3b = 15 ( divide both sides by - 3 )

b = - 5

left sideAs a check

substitute these values into the left side of the equation and if equal to the right side then they are solutions.

b =
`(7)/(3)` : | 3 ×
`(7)/(3)` + 4 | = | 7 + 4 | = | 11 | = 11 = right side

b = - 5 : | 3(- 5) + 4 | = | - 15 + 4 | = | - 11 | = 11 = right side

Then x = - 5 and x =
`(7)/(3)` are the solutions of the equation