Solve for all values of x in simplest form. 5-4|2x-3|=-11 Answer: x=

Isolate Absolute Value: Isolate the absolute value expression. Add 4|2x - 3| to both sides to isolate the absolute value on one side. 5 - 4|2x - 3| + 4|2x - 3| = -11 + 4|2x - 3| 5 + 4|2x - 3| = -11 + 4|2x - 3| 5 + 4|2x - 3| = -11 + 4|2x - 3| 5 = -11 + 4|2x - 3|Simplify Equation: Simplify the equation. Subtract 5 from both sides to get the absolute value by itself. 5 - 5 = -11 + 4|2x - 3| - 5 0 = -16 + 4|2x - 3|Add 16 and Solve: Add 16 to both sides to solve for the absolute value. 0 + 16 = -16 + 16 + 4|2x - 3| 16 = 4|2x - 3|Divide and Find Value: Divide both sides by 4 to find the value of the absolute value expression. 16 / 4 = 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 = -4Solve for x (1st): Solve the first equation for x. 2x - 3 = 4 Add 3 to both sides. 2x - 3 + 3 = 4 + 3 2x = 7 Divide both sides by 2. 2x / 2 = 7 / 2 x = 7/2Solve for x (2nd): Solve the second equation for x. 2x - 3 = -4 Add 3 to both sides. 2x - 3 + 3 = -4 + 3 2x = -1 Divide both sides by 2. 2x / 2 = -1 / 2 x = -1/2

Home

Math Problems

Algebra 2

Solve absolute value equations

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 = $-\frac{1}{2}$