Solve the equation for all values of x. |x+6|=2x Answer: x=

Absolute Value Equation: We have the equation |x+6|=2x. To solve this, we need to consider two cases because the absolute value function yields the same result for both the positive and negative values of its argument.Case 1: Non-Negative Expression: Case 1 - When the expression inside the absolute value is non-negative, we can remove the absolute value bars without changing the sign of the expression. So, we have: x + 6 = 2x Now, we solve for x. Subtract x from both sides to get: 6 = xCase 2: Negative Expression: Case 2 - When the expression inside the absolute value is negative, we remove the absolute value bars and change the sign of the expression. So, we have: -(x + 6) = 2x Simplify and solve for x: -x - 6 = 2x Add x to both sides to get: -6 = 3x Now, divide both sides by 3 to get: x = -2Solution Verification for x = 6: We need to check if our solutions satisfy the original equation. For x = 6, we substitute into the original equation: |6 + 6| = 2(6) |12| = 12 12 = 12, which is true.Solution Verification for x = -2: Now, we check the solution x = -2: |-2 + 6| = 2(-2) |4| = -4 4 ≠ -4, which is false. Therefore, x = -2 is not a solution to the equation.

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Solve the equation for all values of
x.

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

Solve the equation for all values of $x$ . $\newline$ $|x+6|=2 x$ $\newline$ Answer: $x=$

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Grade 8

Evaluate absolute value expressions

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Q. Solve the equation for all values of

x

\newline

|x+6|=2 x

\newline

Answer:

x=

Absolute Value Equation: We have the equation $|x+6|=2x$ . To solve this, we need to consider two cases because the absolute value function yields the same result for both the positive and negative values of its argument.
Case $1$ : Non-Negative Expression: Case $1$ - When the expression inside the absolute value is non-negative, we can remove the absolute value bars without changing the sign of the expression. So, we have: $\newline$ $x + 6 = 2x$ $\newline$ Now, we solve for $x$ . $\newline$ Subtract $x$ from both sides to get: $\newline$ $6 = x$
Case $2$ : Negative Expression: Case $2$ - When the expression inside the absolute value is negative, we remove the absolute value bars and change the sign of the expression. So, we have: $\newline$ $- (x + 6) = 2x$ $\newline$ Simplify and solve for $x$ : $\newline$ $-x - 6 = 2x$ $\newline$ Add $x$ to both sides to get: $\newline$ $-6 = 3x$ $\newline$ Now, divide both sides by $3$ to get: $\newline$ $x = -2$
Solution Verification for $x = 6$ : We need to check if our solutions satisfy the original equation. For $x = 6$ , we substitute into the original equation: $\newline$ $|6 + 6| = 2(6)$ $\newline$ $|12| = 12$ $\newline$ $12 = 12$ , which is true.
Solution Verification for $x = -2$ : Now, we check the solution $x = -2$ :
$|-2 + 6| = 2(-2)$
$|4| = -4$
$4 \neq -4$ , which is false. Therefore, $x = -2$ is not a solution to the equation.