Solve each equation. See Examples 4–6. √(3x+7) = 3x+5

Key Concepts

Square Roots

A square root of a number is a value that, when multiplied by itself, gives the original number. In the equation √(3x+7) = 3x+5, understanding how to manipulate square roots is essential. This includes knowing that squaring both sides of the equation can eliminate the square root, leading to a polynomial equation that can be solved.

Isolating Variables

Isolating variables involves rearranging an equation to get the variable of interest on one side. In this case, after squaring both sides, you will need to combine like terms and isolate 'x' to find its value. This concept is fundamental in algebra as it allows for solving equations systematically.

Checking Solutions

After finding potential solutions for an equation, it is crucial to check them by substituting back into the original equation. This step ensures that the solutions are valid, especially when squaring both sides, which can introduce extraneous solutions. Verifying solutions helps confirm their correctness in the context of the problem.