Solve for all values of x in simplest form. |5x-4|-8=2 Answer: x=

Isolate absolute value: First, we need to isolate the absolute value expression on one side of the equation. Add 8 to both sides of the equation to isolate the absolute value. |5x - 4| - 8 + 8 = 2 + 8 |5x - 4| = 10Consider two cases: Now, we need to consider the two cases for the absolute value expression. Case 1: The expression inside the absolute value is positive or zero. 5x - 4 = 10Solve Case 1: Solve for x in Case 1. Add 4 to both sides of the equation. 5x - 4 + 4 = 10 + 4 5x = 14 Divide both sides by 5. x = 14 / 5 x = 2.8Solve Case 2: Case 2: The expression inside the absolute value is negative. 5x - 4 = -10Solve for x in Case 2. Add 4 to both sides of the equation. 5x - 4 + 4 = -10 + 4 5x = -6 Divide both sides by 5. x = -6 / 5 x = -1.2

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Solve for all values of
x in simplest form.

|5x-4|-8=2
Answer:
x=

Solve for all values of $x$ in simplest form. $\newline$ $|5 x-4|-8=2$ $\newline$ Answer: $x=$

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Math Problems

Grade 8

Evaluate absolute value expressions

Full solution

Q. Solve for all values of

x

in simplest form.

\newline

|5 x-4|-8=2

\newline

Answer:

x=

Isolate absolute value: First, we need to isolate the absolute value expression on one side of the equation. $\newline$ Add $8$ to both sides of the equation to isolate the absolute value. $\newline$ $|5x - 4| - 8 + 8 = 2 + 8$ $\newline$ $|5x - 4| = 10$
Consider two cases: Now, we need to consider the two cases for the absolute value expression. $\newline$ Case $1$ : The expression inside the absolute value is positive or zero. $\newline$ $5x - 4 = 10$
Solve Case $1$ : Solve for $x$ in Case $1$ . $\newline$ Add $4$ to both sides of the equation. $\newline$ $5x - 4 + 4 = 10 + 4$ $\newline$ $5x = 14$ $\newline$ Divide both sides by $5$ . $\newline$ $x = \frac{14}{5}$ $\newline$ $x = 2.8$
Solve Case $2$ : Case $2$ : The expression inside the absolute value is negative. $\newline$ $5x - 4 = -10$
Solve Case $2$ : Case $2$ : The expression inside the absolute value is negative. $\newline$ $5x - 4 = -10$ Solve for $x$ in Case $2$ . $\newline$ Add $4$ to both sides of the equation. $\newline$ $5x - 4 + 4 = -10 + 4$ $\newline$ $5x = -6$ $\newline$ Divide both sides by $5$ . $\newline$ $x = -6 / 5$ $\newline$ $x = -1.2$