How to solve | 7 p + 4 | 8 = 3 ?

Question

How to solve                     |                  7          p          +          4                |            8        =    3  ?

Marley Rowe · Accepted Answer

The absolute value may have a positive or a negative result, as long as it is equal

8 \times 3

In order to isolate and determine p, multiply both sides by 8 first.
Take the absolute value term's positive value first.

{+ \frac{7 p + 4}{8}} \times 8 = 3 \times 8

This gives
7p + 4 = 24 Subtract 4 from both sides
7p + 4 - 4 = 24 - 4 This gives
7p = 20 Divide both sides by 7

7 \frac{p}{7}

=

\frac{20}{7}

This gives p =

\frac{20}{7}

Now take the negative value of the absolute value term.

{- \frac{7 p + 4}{8}) \times 8 = 3 \times 8

This gives
7p -4 = 24 add 4 to both sides
7p - 4 + 4 = 24 + 4 This gives
-7p = 28 divide both sides by -7

- 7 \frac{p}{- 7} = \frac{28}{- 7}

This gives
p = -4

How to solve (|7p+4|)/8 =3?