Solve for all values of x in simplest form. 1+5|6-3x|=26 Answer: x=

Isolate absolute value expression: Start by isolating the absolute value expression on one side of the equation. Subtract 1 from both sides of the equation to get: 1 + 5|6 - 3x| - 1 = 26 - 1 5|6 - 3x| = 25Divide by 5: Divide both sides of the equation by 5 to solve for the absolute value expression. 5|6 - 3x| / 5 = 25 / 5 |6 - 3x| = 5Set up two equations: Set up two separate equations to account for the two possible cases of the absolute value (one where the expression inside is positive and one where it is negative). Case 1: 6 - 3x = 5 Case 2: 6 - 3x = -5Solve for x in Case 1: Solve for x in Case 1. 6 - 3x = 5 Subtract 6 from both sides: -3x = 5 - 6 -3x = -1 Divide both sides by -3: x = -1 / -3 x = 1/3Solve for x in Case 2: Solve for x in Case 2. 6 - 3x = -5 Subtract 6 from both sides: -3x = -5 - 6 -3x = -11 Divide both sides by -3: x = -11 / -3 x = 11/3

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Solve for all values of
x in simplest form.

1+5|6-3x|=26
Answer:
x=

Solve for all values of $x$ in simplest form. $\newline$ $1+5|6-3 x|=26$ $\newline$ 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

1+5|6-3 x|=26

\newline

Answer:

x=

Isolate absolute value expression: Start by isolating the absolute value expression on one side of the equation. $\newline$ Subtract $1$ from both sides of the equation to get: $\newline$ $1 + 5|6 - 3x| - 1 = 26 - 1$ $\newline$ $5|6 - 3x| = 25$
Divide by $5$ : Divide both sides of the equation by $5$ to solve for the absolute value expression. $\newline$ $\frac{5|6 - 3x|}{5} = \frac{25}{5}$ $\newline$ $|6 - 3x| = 5$
Set up two equations: Set up two separate equations to account for the two possible cases of the absolute value (one where the expression inside is positive and one where it is negative). $\newline$ Case $1$ : $6 - 3x = 5$ $\newline$ Case $2$ : $6 - 3x = -5$
Solve for x in Case $1$ : Solve for x in Case $1$ . $\newline$ $6 - 3x = 5$ $\newline$ Subtract $6$ from both sides: $\newline$ $-3x = 5 - 6$ $\newline$ $-3x = -1$ $\newline$ Divide both sides by $-3$ : $\newline$ $x = -1 / -3$ $\newline$ $x = 1/3$
Solve for x in Case $2$ : Solve for x in Case $2$ . $\newline$ $6 - 3x = -5$ $\newline$ Subtract $6$ from both sides: $\newline$ $-3x = -5 - 6$ $\newline$ $-3x = -11$ $\newline$ Divide both sides by $-3$ : $\newline$ $x = \frac{-11}{-3}$ $\newline$ $x = \frac{11}{3}$