Solve for all values of x in simplest form. 31=|10-3x| Answer: x=

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Solve for all values of  x in simplest form.  31=|10-3x| Answer:  x=

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Understand absolute value equation: Understand the absolute value equation The absolute value of a number is its distance from zero on the number line, regardless of direction. Therefore, |10 - 3x| can be either 10 - 3x or -(10 - 3x) if 10 - 3x is negative. We need to consider both cases to find all values of x.Set up two equations: Set up two equations Since the absolute value expression can be positive or negative, we set up two equations to solve for x: 1) 10 - 3x = 31 2) -(10 - 3x) = 31Solve first equation: Solve the first equation Solve 10 - 3x = 31 for x: Subtract 10 from both sides: -3x = 31 - 10 -3x = 21 Divide both sides by -3: x = 21 / -3 x = -7Solve second equation: Solve the second equation Solve -(10 - 3x) = 31 for x: First, distribute the negative sign: -10 + 3x = 31 Add 10 to both sides: 3x = 31 + 10 3x = 41 Divide both sides by 3: x = 41 / 3 x = 13.666...Combine the solutions: Combine the solutions The solutions from both equations are x = -7 and x = 13.666..., which can also be written as x = 41/3.

Solve for all values of $x$ in simplest form. $\newline$ $31=|10-3 x|$ $\newline$ Answer: $x=$

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Solve for all values of $x$ in simplest form. $\newline$ $31=|10-3 x|$ $\newline$ Answer: $x=$