Solve for all values of x in simplest form. 16=|-3x+3| Answer: x=

Given Equation: We are given the equation 16 = |-3x + 3|. The absolute value equation can be split into two separate equations, one for the positive case and one for the negative case.Positive Case: First, let's consider the positive case. We remove the absolute value and keep the expression inside the same: 16 = -3x + 3 Now, we will solve for x.Solving for x: Subtract 3 from both sides of the equation to isolate the term with x: 16 - 3 = -3x + 3 - 3 13 = -3xNegative Case: Divide both sides by -3 to solve for x: 13 / -3 = -3x / -3 x = -13/3Solving for x: Now, let's consider the negative case. We remove the absolute value and make the expression inside negative: 16 = -(-3x + 3) 16 = 3x - 3Add 3 to both sides of the equation to isolate the term with x: 16 + 3 = 3x - 3 + 3 19 = 3xDivide both sides by 3 to solve for x: 19 / 3 = 3x / 3 x = 19/3

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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

16=|-3 x+3|

\newline

Answer:

x=

Given Equation: We are given the equation $16 = |-3x + 3|$ . The absolute value equation can be split into two separate equations, one for the positive case and one for the negative case.
Positive Case: First, let's consider the positive case. We remove the absolute value and keep the expression inside the same: $16 = -3x + 3$ Now, we will solve for $x$ .
Solving for x: Subtract $3$ from both sides of the equation to isolate the term with $x$ : $\newline$ $16 - 3 = -3x + 3 - 3$ $\newline$ $13 = -3x$
Negative Case: Divide both sides by $-3$ to solve for $x$ : $\frac{13}{-3} = \frac{-3x}{-3}$ $x = -\frac{13}{3}$
Solving for x: Now, let's consider the negative case. We remove the absolute value and make the expression inside negative: $\newline$ $16 = -( -3x + 3)$ $\newline$ $16 = 3x - 3$
Solving for x: Now, let's consider the negative case. We remove the absolute value and make the expression inside negative: $\newline$ $16 = -( -3x + 3)$ $\newline$ $16 = 3x - 3$ Add $3$ to both sides of the equation to isolate the term with x: $\newline$ $16 + 3 = 3x - 3 + 3$ $\newline$ $19 = 3x$
Solving for x: Now, let's consider the negative case. We remove the absolute value and make the expression inside negative: $\newline$ $16 = -( -3x + 3)$ $\newline$ $16 = 3x - 3$ Add $3$ to both sides of the equation to isolate the term with x: $\newline$ $16 + 3 = 3x - 3 + 3$ $\newline$ $19 = 3x$ Divide both sides by $3$ to solve for x: $\newline$ $\frac{19}{3} = \frac{3x}{3}$ $\newline$ $x = \frac{19}{3}$