Solve the equation for all values of x. |x+1|+7=2x Answer: x=

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Solve the equation for all values of  x.  |x+1|+7=2x Answer:  x=

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Introduction: We have the equation |x+1| + 7 = 2x. To solve for x, we need to consider two cases because the absolute value function yields two possible scenarios: one where the expression inside the absolute value is non-negative (x+1 ≥ 0) and one where it is negative (x+1 < 0).Case 1: Non-negative x: First, let's consider the case where x+1 is non-negative, which means x+1 ≥ 0 or x ≥ -1. In this case, the absolute value function does not change the sign of the expression inside it. So, we have x+1 + 7 = 2x. Now, let's solve for x. x + 1 + 7 = 2x x + 8 = 2x Subtract x from both sides: 8 = xCase 2: Negative x: Now, let's consider the case where x+1 is negative, which means x+1 < 0 or x < -1. In this case, the absolute value function will change the sign of the expression inside it. So, we have -(x+1) + 7 = 2x. Now, let's solve for x. -(x + 1) + 7 = 2x - x - 1 + 7 = 2x 6 - x = 2x Add x to both sides: 6 = 3x Divide both sides by 3: 2 = xSolutions Analysis: We have found two potential solutions, x = 8 and x = 2. However, we must check these solutions against the original conditions we set for each case. For x = 8, the condition was x ≥ -1, which is true. For x = 2, the condition was x < -1, which is not true. Therefore, x = 2 is not a valid solution to the original equation.Valid Solution: The only solution that satisfies the original equation and the conditions we set is x = 8.

Solve the equation for all values of $x$ . $\newline$ $|x+1|+7=2 x$ $\newline$ Answer: $x=$

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Solve the equation for all values of $x$ . $\newline$ $|x+1|+7=2 x$ $\newline$ Answer: $x=$