Question

solve each equation for the given variable.
7.) $-8 + \sqrt{5x - 5} = -3$
8.) $10\sqrt{9x} = 60$

Explanation:

For Equation 7: $-8 + \sqrt{5x - 5} = -3$

Step1: Isolate the radical term

Add 8 to both sides.
$\sqrt{5x - 5} = -3 + 8$
$\sqrt{5x - 5} = 5$

Step2: Eliminate the square root

Square both sides of the equation.
$(\sqrt{5x - 5})^2 = 5^2$
$5x - 5 = 25$

Step3: Isolate the linear term

Add 5 to both sides.
$5x = 25 + 5$
$5x = 30$

Step4: Solve for $x$

Divide both sides by 5.
$x = \frac{30}{5}$
$x = 6$

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For Equation 8: $10\sqrt{9x} = 60$

Step1: Isolate the radical term

Divide both sides by 10.
$\sqrt{9x} = \frac{60}{10}$
$\sqrt{9x} = 6$

Step2: Simplify and solve for $x$

Square both sides, then isolate $x$.
$(\sqrt{9x})^2 = 6^2$
$9x = 36$
$x = \frac{36}{9}$
$x = 4$

Answer:

7.) $x = 6$
8.) $x = 4$