Solve for all values of x in simplest form. 2-5|7+2x|=-23 Answer: x=

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Solve for all values of  x in simplest form.  2-5|7+2x|=-23 Answer:  x=

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Isolate absolute value expression: Start by isolating the absolute value expression on one side of the equation. We have the equation 2 - 5|7 + 2x| = -23. Add 5|7 + 2x| to both sides to move the absolute value expression to one side. 2 - 5|7 + 2x| + 5|7 + 2x| = -23 + 5|7 + 2x| This simplifies to: 2 = -23 + 5|7 + 2x|Add and simplify: Now, subtract 2 from both sides to isolate the term with the absolute value. 2 - 2 = -23 + 5|7 + 2x| - 2 This simplifies to: 0 = -25 + 5|7 + 2x|Subtract to isolate: Next, add 25 to both sides to solve for the absolute value expression. 0 + 25 = -25 + 25 + 5|7 + 2x| This simplifies to: 25 = 5|7 + 2x|Add to solve for absolute value: Divide both sides by 5 to solve for the absolute value of 7 + 2x. 25 / 5 = (5|7 + 2x|) / 5 This simplifies to: 5 = |7 + 2x|Divide to solve for absolute value: Now we have an absolute value equation |7 + 2x| = 5. This means that 7 + 2x can be either 5 or -5. We will solve for x in both cases. First, let's consider 7 + 2x = 5. Subtract 7 from both sides: 7 + 2x - 7 = 5 - 7 This simplifies to: 2x = -2Consider absolute value equation: Divide both sides by 2 to solve for x. 2x / 2 = -2 / 2 This simplifies to: x = -1Solve for x (1st case): Now let's consider the second case where 7 + 2x = -5. Subtract 7 from both sides: 7 + 2x - 7 = -5 - 7 This simplifies to: 2x = -12Divide to solve for x (1st case): Divide both sides by 2 to solve for x. 2x / 2 = -12 / 2 This simplifies to: x = -6

Solve for all values of $x$ in simplest form. $\newline$ $2-5|7+2 x|=-23$ $\newline$ Answer: $x=$

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Solve for all values of $x$ in simplest form. $\newline$ $2-5|7+2 x|=-23$ $\newline$ Answer: $x=$