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

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

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Absolute Value Equation: We have the equation |2x + 6| = x. To solve this, we need to consider two cases because the absolute value function outputs the input value if it's non-negative, and the negation of the input value if it's negative.Case 1 Solution: Case 1: If 2x + 6 is non-negative, then |2x + 6| = 2x + 6. So we have the equation 2x + 6 = x. Now, we solve for x. Subtract x from both sides to get x + 6 = 0. Subtract 6 from both sides to get x = -6.Case 2 Solution: Case 2: If 2x + 6 is negative, then |2x + 6| = -(2x + 6). So we have the equation -(2x + 6) = x. Now, we solve for x. Distribute the negative sign to get -2x - 6 = x. Add 2x to both sides to get -6 = 3x. Divide both sides by 3 to get x = -2.Check Validity: We need to check if our solutions make the original equation true. For x = -6, substituting into the original equation gives |2(-6) + 6| = -6, which simplifies to |-12 + 6| = -6, and further to |-6| = -6. Since the absolute value of a number cannot be negative, x = -6 is not a valid solution.Final Solution: For x = -2, substituting into the original equation gives |2(-2) + 6| = -2, which simplifies to |-4 + 6| = -2, and further to |2| = -2. Since the absolute value of a number cannot be negative, x = -2 is not a valid solution either.

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

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