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

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.

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

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

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

Final Answer