Subtract seven on both sides.

\(\displaystyle \sqrt{5x-4} +7 -7= 10-7\)

\(\displaystyle \sqrt{5x-4} =3\)

Square both sides.  This will eliminate the radical on the left side.

\(\displaystyle (\sqrt{5x-4} )^2=3^2\)

\(\displaystyle 5x-4 = 9\)

Add four on both sides.

\(\displaystyle 5x-4 +4= 9+4\)

\(\displaystyle 5x=13\)

Divide by five on both sides.

\(\displaystyle \frac{5x}{5}=\frac{13}{5}\)

The answer is:  \(\displaystyle \frac{13}{5}\)

Add three on both sides.

\(\displaystyle 3\sqrt[3]{4x-3} -3+3= 1+3\)

\(\displaystyle 3\sqrt[3]{4x-3}=4\)

Divide by three on both sides.

\(\displaystyle \frac{3\sqrt[3]{4x-3}}{3}=\frac{4}{3}\)

\(\displaystyle \sqrt[3]{4x-3}=\frac{4}{3}\)

Cube both sides to eliminate the radical.  Simplify both sides.

\(\displaystyle (\sqrt[3]{4x-3})^3=(\frac{4}{3})^3\)

\(\displaystyle 4x-3 = \frac{64}{27}\)

Add three on both sides.  This is the same as adding \(\displaystyle \frac{81}{27}\) on the right side.

\(\displaystyle 4x-3+3=\frac{64}{27}+\frac{81}{27}\)

\(\displaystyle 4x= \frac{145}{27}\)

Divide by four on both sides.  This is similar to multiplying one fourth on both sides and will isolate the x-variable on the left.

\(\displaystyle 4x\cdot \frac{1}{4}= \frac{145}{27}\cdot \frac{1}{4}\)

\(\displaystyle x=\frac{145}{108}\)

The answer is:  \(\displaystyle \frac{145}{108}\)

In order to solve this equation, first add 28 on both sides.

\(\displaystyle \sqrt{6x-3}-28+28 = 30+28\)

\(\displaystyle \sqrt{6x-3}=58\)

Square both sides.

\(\displaystyle (\sqrt{6x-3})^2=58^2\)

\(\displaystyle 6x-3=3364\)

Add three on both sides.

\(\displaystyle 6x-3+3=3364+3\)

\(\displaystyle 6x=3367\)

Divide by six on both sides.

\(\displaystyle \frac{6x}{6}=\frac{3367}{6}\)

The answer is:  \(\displaystyle \frac{3367}{6}\)

Cube both sides.

\(\displaystyle (\sqrt[3]{6x-2})^3= 4^3\)

This will eliminate the radical.

\(\displaystyle 6x-2= 64\)

Add two on both sides.

\(\displaystyle 6x-2+2= 64+2\)

\(\displaystyle 6x=66\)

Divide by six on both sides.

\(\displaystyle \frac{6x}{6}=\frac{66}{6}\)

The answer is:  \(\displaystyle 11\)

Raise both sides of the equation by five.

\(\displaystyle (\sqrt[5]{2x-6} )^5= 2^5\)

\(\displaystyle 2x-6 = 32\)

Add six on both sides.

\(\displaystyle 2x-6 +6= 32+6\)

\(\displaystyle 2x=38\)

Divide by two on both sides.

\(\displaystyle \frac{2x}{2}=\frac{38}{2}\)

Simplify both sides.

The answer is:  \(\displaystyle 19\)

Square both sides to eliminate the radical.

\(\displaystyle (\sqrt{\frac{3}{2}x-1} )^2= 5^2\)

The equation becomes:

\(\displaystyle \frac{3}{2}x-1 = 25\)

Add one on both sides.

\(\displaystyle \frac{3}{2}x-1 +1= 25+1\)

\(\displaystyle \frac{3}{2}x = 26\)

Multiply two-thirds on both sides to isolate the x-variable.

\(\displaystyle \frac{3}{2}x \cdot \frac{2}{3}= 26\cdot \frac{2}{3}\)

Simplify both sides.

The answer is:  \(\displaystyle \frac{52}{3}\)

Subtract both sides by four.

\(\displaystyle \frac{2}{\sqrt{2x}}+4-4=8-4\)

\(\displaystyle \frac{2}{\sqrt{2x}}=4\)

Multiply by the denominator on both sides.  The equation becomes:

\(\displaystyle 2=4\sqrt{2x}\)

Divide by four on both sides to isolate the radical.

\(\displaystyle \frac{2}{4}=\frac{4\sqrt{2x}}{4}\)

\(\displaystyle \frac{1}{2} = \sqrt{2x}\)

Square both sides.

\(\displaystyle \frac{1}{4} = 2x\)

Divide by two on both sides.

The answer is:  \(\displaystyle \frac{1}{8}\)

Subtract three on both sides.

\(\displaystyle \sqrt[5]{9x-3}+3 -3= 5-3\)

\(\displaystyle \sqrt[5]{9x-3} = 2\)

Take the fifth power of both sides to cancel the radical.

\(\displaystyle (\sqrt[5]{9x-3})^5 = 2^5\)

\(\displaystyle 9x-3 = 32\)

Add three on both sides.

\(\displaystyle 9x-3 +3= 32+3\)

\(\displaystyle 9x=35\)

Divide by nine on both sides.

\(\displaystyle \frac{9x}{9}=\frac{35}{9}\)

The answer is:  \(\displaystyle \frac{35}{9}\)

Square both sides to eliminate the radical.

\(\displaystyle (\sqrt{3x-9} )^2= 27^{2}\)

\(\displaystyle 3x-9 = 729\)

Add 9 on both sides.

\(\displaystyle 3x=738\)

Divide by three on both sides.

\(\displaystyle \frac{3x}{3}=\frac{738}{3}\)

The answer is:  \(\displaystyle 246\)

Add 7 on both sides.

\(\displaystyle \sqrt{9x-2}-7+7 =1+7\)

\(\displaystyle \sqrt{9x-2} =8\)

Square both sides.

\(\displaystyle (\sqrt{9x-2}) ^2=8^2\)

Simplify both sides of the equation.

\(\displaystyle 9x-2 =64\)

Add 2 on both sides.

\(\displaystyle 9x-2+2 =64+2\)

\(\displaystyle 9x=66\)

Divide by nine on both sides.

\(\displaystyle \frac{9x}{9}=\frac{66}{9}\)

Reduce both fractions.

\(\displaystyle x=\frac{66}{9}=\frac{3\times 11\times 2}{3\times 3} =\frac{22}{3}\)

The answer is:  \(\displaystyle \frac{22}{3}\)