Problem

QUESTION 3 - 1 POINT Find the solutions to the following absolute value equation. \[ 7|x+5|+4=8 \] Separate multiple answers with a comma. Provide your answer below: \[ x= \]

Solution

Step 1 :First, isolate the absolute value expression by subtracting 4 from both sides of the equation to get \(7|x+5|=4\). Then, divide both sides by 7 to get \(|x+5| = \frac{4}{7}\).

Step 2 :Next, split the equation into two separate equations, one for the positive value and one for the negative value of the absolute value expression. This gives us \(x+5 = \frac{4}{7}\) and \(-x-5 = \frac{4}{7}\).

Step 3 :Solve each equation separately to find the solutions. Solving the first equation gives \(x = -\frac{31}{7}\). Solving the second equation gives \(x = -\frac{39}{7}\).

Step 4 :Final Answer: The solutions to the equation are \(x= \boxed{-\frac{31}{7}, -\frac{39}{7}}\).

From Solvely APP
Source: https://solvelyapp.com/problems/46146/

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