Questions: 2x + 7 - 8 = -5

Transcript text: 43. $|2 x+7|-8=-5$

Solution

Solution Steps

To solve the equation $ |2x + 7| - 8 = -5 $, we first isolate the absolute value expression. Then, we set up two separate equations to account for the positive and negative scenarios of the absolute value. Finally, we solve each equation for $ x $.

Step 1: Isolate the Absolute Value Expression

The given equation is:

\[ |2x + 7| - 8 = -5 \]

First, we need to isolate the absolute value expression by adding 8 to both sides of the equation:

\[ |2x + 7| = -5 + 8 \]

Simplifying the right side gives:

\[ |2x + 7| = 3 \]

Step 2: Solve the Absolute Value Equation

The equation $|2x + 7| = 3$ implies two possible cases:

Case 1: Positive Case

\[ 2x + 7 = 3 \]

Subtract 7 from both sides:

\[ 2x = 3 - 7 \]

\[ 2x = -4 \]

Divide both sides by 2:

\[ x = -2 \]

Case 2: Negative Case

\[ 2x + 7 = -3 \]

Subtract 7 from both sides:

\[ 2x = -3 - 7 \]

\[ 2x = -10 \]

Divide both sides by 2:

\[ x = -5 \]

Final Answer

The solutions to the equation are:

\[ \boxed{x = -2} \]

\[ \boxed{x = -5} \]

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