Solve |4y-9|=|26-5sqrt{64}|

$$| 4 y - 9 | = | 26 - 5 \sqrt { 64 } |$$

Solve for y

$$y = -\frac{5}{4} = -1\frac{1}{4} = -1.25$$

$$y = \frac{23}{4} = 5\frac{3}{4} = 5.75$$

Steps Using Definition of Absolute Value

Calculate the square root of 64 and get 8.

$$|4y-9|=|26-5\times 8|$$

Multiply -5 and 8 to get -40.

$$|4y-9|=|26-40|$$

Subtract 40 from 26 to get -14.

$$|4y-9|=|-14|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -14 is 14.

$$|4y-9|=14$$

Use the definition of absolute value.

$$4y-9=14 4y-9=-14$$

Add 9 to both sides of the equation.

$$4y=23 4y=-5$$

Divide both sides by 4.

$$y=\frac{23}{4} y=-\frac{5}{4}$$