how do i solve 4+| R+2 |=7 ?

Question

this is absolute value.

Answer 1

The equation is 4+|R+2| = 7 .

First rewrite the above equation in the form |ax+b| = c where c ≥0 and it is equivalent to the statement  ax+b = c or ax+b = - c.

Subtract 4 from each side.

4+|R+2|- 4 = 7- 4

|R+2| = 3.

Rewrite the equation |R+2| = 3 as two equations R+2 = 3 or R+2 = -3.

Then solve each equation separately.

Solve the equation 1: R+2 = 3.

Subtract 2 from each side.

R+2 -2 = 3 -2

R =1.

Solve the equation 2: R+2 = -3.

Subtract 2 from each side.

R+2 -2 = -3 -2

R =  -5.

The solutions of the equation are 1 and -5.