Questions: 2x+3+4=34

2x+3+4=34
Transcript text: $2|x+3|+4=34$
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Solution

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Solution Steps

To solve the equation \(2|x+3|+4=34\), we first isolate the absolute value expression. Subtract 4 from both sides to get \(2|x+3| = 30\). Then, divide both sides by 2 to obtain \(|x+3| = 15\). This absolute value equation implies two possible linear equations: \(x+3 = 15\) and \(x+3 = -15\). Solve each equation separately to find the values of \(x\).

Step 1: Isolate the Absolute Value

Starting with the equation: \[ 2|x+3| + 4 = 34 \] we first subtract 4 from both sides: \[ 2|x+3| = 30 \]

Step 2: Solve for the Absolute Value

Next, we divide both sides by 2: \[ |x+3| = 15 \]

Step 3: Set Up the Linear Equations

The absolute value equation \( |x+3| = 15 \) leads to two cases:

  1. \( x + 3 = 15 \)
  2. \( x + 3 = -15 \)
Step 4: Solve Each Case

For the first case: \[ x + 3 = 15 \implies x = 15 - 3 = 12 \]

For the second case: \[ x + 3 = -15 \implies x = -15 - 3 = -18 \]

Final Answer

The solutions to the equation are: \[ \boxed{x = 12} \quad \text{and} \quad \boxed{x = -18} \]

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