Questions: Solve for x . [ sqrt3 x-1=7 ] What is the root? If there is no root, choose none. 16 2/3 16 12 none

Solution Steps

To solve the equation \(\sqrt{3x - 1} = 7\), we need to eliminate the square root by squaring both sides of the equation. This will give us a linear equation in terms of \(x\). After solving for \(x\), we should verify if the solution satisfies the original equation.

We start with the equation: \[ \sqrt{3x - 1} = 7 \] To eliminate the square root, we square both sides: \[ 3x - 1 = 7^2 \] This simplifies to: \[ 3x - 1 = 49 \]

Next, we isolate \(x\) by adding 1 to both sides: \[ 3x = 49 + 1 \] This gives us: \[ 3x = 50 \] Now, we divide both sides by 3: \[ x = \frac{50}{3} \]

We need to verify that our solution satisfies the original equation. Substituting \(x = \frac{50}{3}\) back into the original equation: \[ \sqrt{3\left(\frac{50}{3}\right) - 1} = \sqrt{50 - 1} = \sqrt{49} = 7 \] Since both sides are equal, our solution is valid.

Final Answer