How do i algebraically solve |4x-3|=5√(x+4)

Step-by-step explanation:

|4x-3|=5√(x+4)  ⇔ |4x-3|²=5²(√(x+4))²  and x+4 ≥ 0

                         ⇔ (4x-3)² = 25(x+4)  and x+4 ≥ 0  ( because : /a/² = a²)

                         ⇔16x²-24x+9 = 25x +100  and x+4 ≥ 0

                         ⇔ 16x² -49x - 91 =0 and x+4 ≥ 0 quadratic equation

Δ = (-49)²-4(16)(-91) = 8225

two solution : X1 = (49-√8225)/32  ≅ - 1.3 accept (-1.3+4 ≥ 0)

                     X2 = (49+√8225)/32  ≅4.37 accept (4.37+4 ≥ 0)

1/4 and 8/3 because:

the reciprocal if 4 is 1/4 because 4 is used as 4/1 and the opposite of that is 1/4. the opposite of 3/8 is 8/3 so that is the answer.

twenty-six miles over two gallons because the proportion for the original 13 miles to one gallon would be written 13/1 and, doing the same thing to the top and bottom, i multiplied by 2 and got 26/2