When solving $\sqrt{2x - 6} < 4$, why must we first establish the domain restriction $2x - 6 \geq 0$?

To ensure the solution is an integer.

To ensure the radicand is non-negative for a real solution.

Because the inequality sign is 'less than'.

Solving Radical Equations and Inequalities Practice — Grade 8 math

1. When solving $\sqrt{2x - 6} < 4$, why must we first establish the domain restriction $2x - 6 \geq 0$?
- A. To ensure the solution is an integer.
- B. To ensure the radicand is non-negative for a real solution.
- C. Because the inequality sign is 'less than'.
- D. To simplify the algebra.
2. What is the complete solution to the inequality $\sqrt{3x - 5} > 2$? The solution is `x > ___`.
3. True or false: The first step in solving an equation with a fractional exponent is to isolate the power term.
- A. True
- B. False
4. Solve the equation $x^{3/4} = 4$. Round your answer to two decimal places. Your answer is ___.
5. Solve the equation for $w$. Round your answer to the nearest thousandth. $1.3w^{0.3} + 4.7 = 5.2$. $w = \_\_\_$
6. Solve the equation $(3x - 2)^{3/4} = 8$. The value of $x$ is ___.