Questions: Solve for (x) : [ 2 x+5+2=5 x= ]

Transcript text: Solve for $x$ : \[ \begin{array}{l} |2 x+5|+2=5 \\ x= \end{array} \]

Solution

Solution Steps

To solve the equation $|2x + 5| + 2 = 5$, we first isolate the absolute value expression by subtracting 2 from both sides. This gives us $|2x + 5| = 3$. The absolute value equation $|A| = B$ can be split into two separate equations: $A = B$ and $A = -B$. Therefore, we solve the two equations $2x + 5 = 3$ and $2x + 5 = -3$ to find the possible values of $x$.

Step 1: Isolate the Absolute Value Expression

Start with the equation: \[ |2x + 5| + 2 = 5 \] Subtract 2 from both sides to isolate the absolute value: \[ |2x + 5| = 3 \]

Step 2: Solve the Absolute Value Equation

The equation $|A| = B$ can be split into two separate equations: $A = B$ and $A = -B$. Therefore, we have:

$2x + 5 = 3$
$2x + 5 = -3$

Step 3: Solve Each Equation

Solve the first equation: \[ 2x + 5 = 3 \] Subtract 5 from both sides: \[ 2x = -2 \] Divide by 2: \[ x = -1 \]

Solve the second equation: \[ 2x + 5 = -3 \] Subtract 5 from both sides: \[ 2x = -8 \] Divide by 2: \[ x = -4 \]

Final Answer

$\boxed{x = -1, -4}$

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