Solve for all values of x in simplest form. 2=|4x+6| Answer: x=

Absolute Value Equation: We have the equation 2 = |4x + 6|. The absolute value equation means that the expression inside the absolute value, 4x + 6, can be either positive or negative, but its absolute value must be 2. We will consider both cases.Case 1: Positive Expression: First, let's consider the case where the expression inside the absolute value is positive. This gives us the equation 4x + 6 = 2. Now, we will solve for x. Subtract 6 from both sides of the equation to isolate the term with x. 4x + 6 - 6 = 2 - 6 4x = -4 Now, divide both sides by 4 to solve for x. 4x / 4 = -4 / 4 x = -1Case 2: Negative Expression: Next, let's consider the case where the expression inside the absolute value is negative. This gives us the equation -(4x + 6) = 2. Now, we will solve for x. First, distribute the negative sign inside the parentheses. -4x - 6 = 2 Now, add 6 to both sides of the equation to isolate the term with x. -4x - 6 + 6 = 2 + 6 -4x = 8 Finally, divide both sides by -4 to solve for x. -4x / -4 = 8 / -4 x = -2

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Solve for all values of
x in simplest form.

2=|4x+6|
Answer:
x=

Solve for all values of $x$ in simplest form. $\newline$ $2=|4 x+6|$ $\newline$ Answer: $x=$

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Grade 8

Evaluate absolute value expressions

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Q. Solve for all values of

x

in simplest form.

\newline

2=|4 x+6|

\newline

Answer:

x=

Absolute Value Equation: We have the equation $2 = |4x + 6|$ . The absolute value equation means that the expression inside the absolute value, $4x + 6$ , can be either positive or negative, but its absolute value must be $2$ . We will consider both cases.
Case $1$ : Positive Expression: First, let's consider the case where the expression inside the absolute value is positive. This gives us the equation $4x + 6 = 2$ . Now, we will solve for $x$ . $\newline$ Subtract $6$ from both sides of the equation to isolate the term with $x$ . $\newline$ $4x + 6 - 6 = 2 - 6$ $\newline$ $4x = -4$ $\newline$ Now, divide both sides by $4$ to solve for $x$ . $\newline$ $\frac{4x}{4} = \frac{-4}{4}$ $\newline$ $x = -1$
Case $2$ : Negative Expression: Next, let's consider the case where the expression inside the absolute value is negative. This gives us the equation $- (4x + 6) = 2$ . Now, we will solve for $x$ . First, distribute the negative sign inside the parentheses. $-4x - 6 = 2$ Now, add $6$ to both sides of the equation to isolate the term with $x$ . $-4x - 6 + 6 = 2 + 6$ $-4x = 8$ Finally, divide both sides by $-4$ to solve for $x$ . $-4x / -4 = 8 / -4$ $x$ $0$