Solve and graph on a number line. Express the solution set using interval notation. |4𝑥 − 7| − 3 < 10

Question

College Algebra

Answer 1

|4x - 7| - 3 < 10    ~ add three to both sides

|4x - 7| < 13         ~ the absolute value sign means it cant be greater than 13, or less than negative 13

4x - 7 < 13           ~ is one limit, solve for x

and

4x - 7 > - 13       ~ is the other limit, solve for x again


4x < 20       and      4x > - 5

x = 5 and -4/5 

the interval notation means to include (x1, x2) brackets since those are not less than or greater equalities

the set is: (-0.8, 5)