Charlotte, Eva, Abby, Sean

Front

What is the solution to the equation \(\sqrt{x+3} = x-1\)?

Back

No solution. The left side is always non-negative, while the right side can be negative.

Front

How do you solve the equation \(\sqrt{2x-4} + 8 = x + 7\)?

Back

Isolate the square root: \(\sqrt{2x-4} = x - 1\), then square both sides to find \(x = -1, 5\).

Front

What is the first step in solving \(\frac{8}{x-1} + 1 = \frac{10}{x-1}\)?

Back

Combine the fractions: \(\frac{8 + (x-1)}{x-1} = \frac{10}{x-1}\).

Front

What is the solution to the equation \(\sqrt{x^2 + 7} = x + 1\)?

Back

Square both sides to get \(x^2 + 7 = (x + 1)^2\), leading to \(x = 3\).

Front

What does it mean if an equation has 'no solution'?

Back

It means there are no values of the variable that satisfy the equation.

Front

What is the principle behind squaring both sides of an equation?

Back

Squaring both sides can eliminate square roots, but it may introduce extraneous solutions.

Front

How can you check if a solution is valid after solving an equation?

Back

Substitute the solution back into the original equation to verify if both sides are equal.

Front

What is an extraneous solution?

Back

A solution that emerges from the process of solving an equation but does not satisfy the original equation.

Front

What is the domain of the function \(\sqrt{x+3}\)?

Back

The domain is \(x \geq -3\) because the expression under the square root must be non-negative.

Front

How do you isolate a square root in an equation?

Back

Move all other terms to the opposite side of the equation before squaring both sides.