Solve each equation. See Examples 4–6. √(6x+7) - 9 = x-7

Square roots are the values that, when multiplied by themselves, yield the original number. In the equation √(6x+7) - 9 = x - 7, understanding how to manipulate square roots is crucial. This includes isolating the square root on one side of the equation before squaring both sides to eliminate the root.

Isolating variables involves rearranging an equation to get the variable of interest on one side. This is a fundamental skill in algebra, allowing you to solve for unknowns. In the given equation, isolating x requires moving constants and other terms to one side, simplifying the equation step by step.

After solving an equation, it is essential to check the solutions by substituting them back into the original equation. This step ensures that the solutions are valid and do not introduce extraneous solutions, especially when squaring both sides of an equation, which can sometimes lead to false results.