How do I solve this equation?

x = 22/3, x=14

Step-by-step explanation:

Start by isolating whatever is in the absolute value sign; in this case divide either side by 4

4|1-3/4x + 7| =10,

        4            4

|1-3/4x + 7| = 10/4 = 5/2,

now if we apply the absolute value rule we know that 1-3/4x + 7 will be equal to -5/2, and 5/2

1-3/4x + 7 = 5/2 and 1-3/4x + 7 = -5/2

-3/4x + 8 = 5/2,

-3/4x=5/2-8,

-3/4x = 5/2-16/2,

-3/4x = -11/2,

x = -11/2*-4/3 = 44/6 = 22/3

-3/4x+8 = -5/2

-3/4x = -5/2-8

-3/4x = -5/2-16/2

-3/4x = -21/2

x = -21/2*-4/3 = 82/6 = 14

2 5/8 is the final answer! : )