\sqrt(2x-1+7)=10
Solve algebraically showing all steps
To solve the equation \(\sqrt{2x-1+7}=10\), we need to first isolate the square root then square both sides of the equation to eliminate the square root:
1. Add 1 and 7 to simplify the expression:
\(\sqrt{2x+6}=10\)
2. Square both sides of the equation to eliminate the square root:
\((\sqrt{2x+6})^2=10^2\)
\(2x+6=100\)
3. Subtract 6 from both sides:
\(2x=94\)
4. Divide by 2 to solve for x:
\(x=\frac{94}{2}\)
\(x=47\)
Therefore, the solution to the equation \(\sqrt{2x-1+7}=10\) is \(x=47\).