Questions: Solve the equation √(x+3)+4=5 for the variable. Show each step of your solution process.

Solve the equation √(x+3)+4=5 for the variable. Show each step of your solution process.
Transcript text: Solve the equation $\sqrt{x+3}+4=5$ for the variable. Show each step of your solution process.
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Solution

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Solution Steps

To solve the equation \(\sqrt{x+3} + 4 = 5\), we first isolate the square root term by subtracting 4 from both sides. Then, we square both sides to eliminate the square root. Finally, we solve for \(x\) by isolating it on one side of the equation.

Step 1: Isolate the Square Root Term

Start with the equation: \[ \sqrt{x+3} + 4 = 5 \] Subtract 4 from both sides to isolate the square root: \[ \sqrt{x+3} = 1 \]

Step 2: Eliminate the Square Root

Square both sides of the equation to eliminate the square root: \[ (\sqrt{x+3})^2 = 1^2 \] This simplifies to: \[ x + 3 = 1 \]

Step 3: Solve for \(x\)

Subtract 3 from both sides to solve for \(x\): \[ x = 1 - 3 \] \[ x = -2 \]

Final Answer

The solution to the equation is: \[ \boxed{x = -2} \]

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