Question

Use a graphing calculator to graphically solve the radical equation. Check the solution algebraically. $$\sqrt{15-4 x}=2 x$$

Short answer

The solutions are usually dependent on how accurately you capture the intersection points in your graphing calculator so an exact answer cannot be provided. Analytically validate your solution by substituting your \(x\) value(s) back into the original equation.

Step-by-step solution

Graph a function

Enter the function \(y=\sqrt{15-4 x}\) into your graphing calculator. This will give you the graph of the left side of the equation.

Graph another function

Next, enter the function \(y=2x\) into your graphing calculator. This will give you the graph of the right side of the equation.

Find the intersection

Now, find the x-values at which these two functions intersect. This will be your solutions graphically.

Check the solution algebraically

To confirm the solution, replace \(x\) in the equation \(\sqrt{15-4x}=2x\) with the values found in Step 3. If the left and right sides of the equation are equal, then the solutions are correct.