Solve for all values of x in simplest form. 9-2|1-3x|=-15 Answer: x=

Isolate absolute value expression: Start by isolating the absolute value expression on one side of the equation. Add 15 to both sides of the equation to move -15 to the right side. 9 - 2|1 - 3x| + 15 = -15 + 15Simplify equation: Simplify both sides of the equation. 9 + 15 = 24, so the equation becomes: 24 - 2|1 - 3x| = 0Move 24 to other side: Now, isolate the absolute value expression by moving 24 to the other side. -2|1 - 3x| = -24Divide by -2: Divide both sides by -2 to solve for the absolute value expression. |1 - 3x| = 12Set up two equations: Set up two separate equations to account for the absolute value, one for the positive case and one for the negative case. 1 - 3x = 12 and 1 - 3x = -12Solve first equation: Solve the first equation for x. 1 - 3x = 12 Subtract 1 from both sides: -3x = 12 - 1 -3x = 11 Divide both sides by -3: x = 11 / -3 x = -11/3Solve second equation: Solve the second equation for x. 1 - 3x = -12 Subtract 1 from both sides: -3x = -12 - 1 -3x = -13 Divide both sides by -3: x = -13 / -3 x = 13/3

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Solve for all values of
x in simplest form.

9-2|1-3x|=-15
Answer:
x=

Solve for all values of $x$ in simplest form. $\newline$ $9-2|1-3 x|=-15$ $\newline$ 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

9-2|1-3 x|=-15

\newline

Answer:

x=

Isolate absolute value expression: Start by isolating the absolute value expression on one side of the equation. $\newline$ Add $15$ to both sides of the equation to move $-15$ to the right side. $\newline$ $9 - 2|1 - 3x| + 15 = -15 + 15$
Simplify equation: Simplify both sides of the equation. $\newline$ $9 + 15 = 24$ , so the equation becomes: $\newline$ $24 - 2|1 - 3x| = 0$
Move $24$ to other side: Now, isolate the absolute value expression by moving $24$ to the other side. $\newline$ $-2|1 - 3x| = -24$
Divide by $-2$ : Divide both sides by $-2$ to solve for the absolute value expression. $\newline$ $|1 - 3x| = 12$
Set up two equations: Set up two separate equations to account for the absolute value, one for the positive case and one for the negative case. $\newline$ $1 - 3x = 12$ and $1 - 3x = -12$
Solve first equation: Solve the first equation for $x$ . $1 - 3x = 12$ Subtract $1$ from both sides: $-3x = 12 - 1$ $-3x = 11$ Divide both sides by $-3$ : $x = \frac{11}{-3}$ $x = -\frac{11}{3}$
Solve second equation: Solve the second equation for $x$ . $1 - 3x = -12$ Subtract $1$ from both sides: $-3x = -12 - 1$ $-3x = -13$ Divide both sides by $-3$ : $x = -13 / -3$ $x = 13/3$