Full solution

Q. Solve for all values of

x

in simplest form.

\newline

5-4|2 x-3|=-11

\newline

Answer:

x=

Isolate Absolute Value: Isolate the absolute value expression. $\newline$ Add $4|2x - 3|$ to both sides to isolate the absolute value on one side. $\newline$ $5 - 4|2x - 3| + 4|2x - 3| = -11 + 4|2x - 3|$ $\newline$ $5 + 4|2x - 3| = -11 + 4|2x - 3|$ $\newline$ $5 + 4|2x - 3| = -11 + 4|2x - 3|$ $\newline$ $5 = -11 + 4|2x - 3|$
Simplify Equation: Simplify the equation. $\newline$ Subtract $5$ from both sides to get the absolute value by itself. $\newline$ $5 - 5 = -11 + 4|2x - 3| - 5$ $\newline$ $0 = -16 + 4|2x - 3|$
Add $16$ and Solve: Add $16$ to both sides to solve for the absolute value. $\newline$ $0 + 16 = -16 + 16 + 4|2x - 3|$ $\newline$ $16 = 4|2x - 3|$
Divide and Find Value: Divide both sides by $4$ to find the value of the absolute value expression. $\frac{16}{4} = \frac{4|2x - 3|}{4}$ $4 = |2x - 3|$
Set Up Equations: Set up two equations to solve for $x$ , since the absolute value of a number can be either positive or negative. $2x - 3 = 4$ or $2x - 3 = -4$
Solve for x ( $1$ st): Solve the first equation for x. $\newline$ $2x - 3 = 4$ $\newline$ Add $3$ to both sides. $\newline$ $2x - 3 + 3 = 4 + 3$ $\newline$ $2x = 7$ $\newline$ Divide both sides by $2$ . $\newline$ $\frac{2x}{2} = \frac{7}{2}$ $\newline$ x = $\frac{7}{2}$
Solve for x ( $2$ nd): Solve the second equation for x. $\newline$ $2x - 3 = -4$ $\newline$ Add $3$ to both sides. $\newline$ $2x - 3 + 3 = -4 + 3$ $\newline$ $2x = -1$ $\newline$ Divide both sides by $2$ . $\newline$ $\frac{2x}{2} = \frac{-1}{2}$ $\newline$ x = $-\frac{1}{2}$