To solve for \(\displaystyle x\), we need to isolate the variable by having the variable on one side and numbers on the other side.

\(\displaystyle 4(x-15)=2(2x-6)\) Distribute the \(\displaystyle 4,2\) to each term in the parentheses.

\(\displaystyle 4x-60=4x-24\) Because there is \(\displaystyle 4x\) on each side of the equation, they would essentially cancel out leaving us with \(\displaystyle 0=36\) which is not valid.

Answer is no solutions.

Isolate the x-variables on one side of the equation and the integers on the other.

Add \(\displaystyle 2x\) on both sides of the equation.

\(\displaystyle 9x-17+2x=81-2x+2x\)

\(\displaystyle 11x-17=81\)

Add 17 on both sides of the equation.

\(\displaystyle 11x-17+17=81+17\)

Simplify both sides.

\(\displaystyle 11x=98\)

Divide by 11 on both sides.

\(\displaystyle x=\frac{98}{11}\)

The answer is:  \(\displaystyle \frac{98}{11}\)

Use distribution to simplify the left side.

\(\displaystyle 4(x)-4(9) = 30x\)

\(\displaystyle 4x-36=30x\)

Subtract \(\displaystyle 4x\) on both sides.

\(\displaystyle 4x-36-(4x)=30x-(4x)\)

Simplify.

\(\displaystyle -36 = 26x\)

Divide by 26 on both sides.

\(\displaystyle \frac{-36}{26} = \frac{26x}{26}\)

Reduce both fractions.

The answer is:  \(\displaystyle -\frac{18}{13}\)

In order to determine the value of x, we will need to convert the fractions to a least common denominator.

The LCD is 66 because this value is the smallest number that every individual denominator can be divided into.

Convert the fractions.

\(\displaystyle \frac{10(6)}{11(6)}x - \frac{1(2)}{33(2)} = \frac{7}{66}\)

\(\displaystyle \frac{60}{66}x-\frac{2}{66}= \frac{7}{66}\)

Since all the denominators are similar, we can simply set the numerators equal.  Multiplying both sides by 66 will eliminate the denominators.

\(\displaystyle 60x-2=7\)

Add two on both sides.

\(\displaystyle 60x=9\)

Divide by 60 on both sides and reduce the fraction.

\(\displaystyle \frac{60x}{60}=\frac{9}{60}= \frac{3}{20}\)

The answer is:  \(\displaystyle \frac{3}{20}\)

Group the x-variables and integers on a separate side of the equation.

Add \(\displaystyle 18x\) on both sides.

\(\displaystyle 9-18x +(18x)=43+2x+(18x)\)

Simplify the equation.

\(\displaystyle 9=20x+43\)

Subtract \(\displaystyle 43\) on both sides.

\(\displaystyle 9-43=20x+43-43\)

Simplify both sides.

\(\displaystyle -34=20x\)

Divide by twenty on both sides.

\(\displaystyle \frac{-34}{20}=\frac{20x}{20}\)

Reduce both fractions.

The answer is:  \(\displaystyle -\frac{17}{10}\)

Subtract two from both sides.

\(\displaystyle \frac{1}{x}+2-2 =-8-2\)

\(\displaystyle \frac{1}{x}=-10\)

Multiply by \(\displaystyle x\) on both sides.

\(\displaystyle \frac{1}{x} \cdot x=-10 \cdot x\)

\(\displaystyle 1=-10x\)

Divide by negative ten on both sides.

\(\displaystyle \frac{1}{-10}=\frac{-10x}{-10}\)

Simplify both fractions.

The answer is:  \(\displaystyle -\frac{1}{10}\)

Isolate the x-variables on one side and the integers on another.

Add \(\displaystyle 7x\) on both sides of the equation.

\(\displaystyle -7x+38 +(7x)= -5x-50+(7x)\)

Simplify both sides.

\(\displaystyle 38= 2x-50\)

Add 50 on both sides.

\(\displaystyle 38+50= 2x-50+50\)

\(\displaystyle 88=2x\)

Divide by two on both sides.

\(\displaystyle \frac{88}{2}=\frac{2x}{2}\)

The answer is:  \(\displaystyle 44\)

Subtract \(\displaystyle 3x\) from both sides.

\(\displaystyle 9x-6-(3x)=3x+4-(3x)\)

\(\displaystyle 6x-6=4\)

Add six on both sides.

\(\displaystyle 6x-6+6=4+6\)

\(\displaystyle 6x=10\)

Divide by six on both sides.

\(\displaystyle \frac{6x}{6}=\frac{10}{6}\)

Reduce the fractions.

The answer is:  \(\displaystyle \frac{5}{3}\)

Add \(\displaystyle 8x\) on each side.

\(\displaystyle -4x-18 +8x= 46-8x+8x\)

Simplify both sides.

\(\displaystyle 4x-18= 46\)

Add 18 on both sides.

\(\displaystyle 4x-18+18= 46+18\)

\(\displaystyle 4x=64\)

Divide four on both sides.

\(\displaystyle \frac{4x}{4}=\frac{64}{4}\)

The answer is:  \(\displaystyle 16\)

Subtract \(\displaystyle 3x\) on both sides.

\(\displaystyle 6x-18 -3x= 3x-2-3x\)

\(\displaystyle 3x-18 = -2\)

Add 18 on both sides.

\(\displaystyle 3x-18 +18= -2+18\)

\(\displaystyle 3x=16\)

Divide by three on both sides.

\(\displaystyle \frac{3x}{3}=\frac{16}{3}\)

The answer is:  \(\displaystyle \frac{16}{3}\)