Combine like terms on the left side of the equation: \(\displaystyle 2x+2=3(x-1)\)

Use the distributive property to simplify the right side of the equation: \(\displaystyle 2x+2=3x-3\)

Next, move the \(\displaystyle x\)'s to one side and the integers to the other side: \(\displaystyle x=5\)

To solve for \(\displaystyle x\), you must isolate it so that all of the other variables are on the other side of the equation. To do this, first subtract \(\displaystyle f\) from both sides to get \(\displaystyle ex=g-f\). Then, divide both sides by \(\displaystyle e\) to get \(\displaystyle x=\frac{g-f}{e}\).

First you need to subtract 12 from both sides of the equation: 

\(\displaystyle 3x+12-12=36-12.\) 

This gives us 

\(\displaystyle 3x=24.\) 

Then, divide each side by 3:

 \(\displaystyle \frac{3x}{3}=\frac{24}{3}\)  which, when simplified, gives us: 

\(\displaystyle x=8.\)

\(\displaystyle \frac{x}{4} - 3x = 121\)

Step 1: Multiply both sides of the equation by 4.

\(\displaystyle \rightarrow x - 12x = 484\)

Step 2: Combine the \(\displaystyle x\)'s.

\(\displaystyle \rightarrow -11x = 484\)

Step 3: Divide both sides of the equation by -11. 

\(\displaystyle \rightarrow x = -44\)

\(\displaystyle 15 + \frac{y}{2} = 20 - 5y\)

Step 1: Multiply both sides of the equation by 2.

\(\displaystyle \rightarrow 30 + y = 40 - 10 y\)

Step 2: Add \(\displaystyle 10y\) to both sides of the equation, and subtract 30 from both sides of the equation.

\(\displaystyle \rightarrow 11y = 10\)

Step 3: Divide both sides of the equation by 11.

\(\displaystyle \rightarrow y = \frac{10}{11}\)

\(\displaystyle 20 + \frac{2x}{3} = 100\)

Step 1: Multiply both sides of the equation by 3.

\(\displaystyle \rightarrow 60 + 2x = 300\)

Step 2: Subtract 60 from both sides of the equation.

\(\displaystyle \rightarrow 2x = 240\)

Step 3: Divide both sides of the equation by 2.

\(\displaystyle \rightarrow x = 120\)

\(\displaystyle \frac{x}{5} - 22 = -10\)

Step 1: Multiply both sides of the equation by 5.

\(\displaystyle \rightarrow x - 110 = -50\)

Step 2: Add 110 to both sides of the equation.

\(\displaystyle \rightarrow x = 60\)

\(\displaystyle -16 - 4x = \frac{x}{5} + 2x\)

Step 1: Multiply both sides of the equation by 5.

\(\displaystyle \rightarrow -80 - 20x = x + 10x\)

Step 2: Combine the \(\displaystyle x\)'s. 

\(\displaystyle \rightarrow -80 - 20x = 11x\)

Step 3: Add \(\displaystyle 20x\) to both sides of the equation.

\(\displaystyle \rightarrow -80 = 31x\)

Step 4: Divide both sides of the equation by 31.

\(\displaystyle \rightarrow x = -\frac{80}{31}\)

\(\displaystyle 48 = \frac{x}{2}+ 20\)

Step 1: Multiply both sides of the equation by 2.

\(\displaystyle \rightarrow 96 = x + 40\)

Step 2: Subtract 40 from both sides of the equation.

\(\displaystyle \rightarrow x = 56\)

\(\displaystyle 5 + \frac{3}{x} = 20\)

Step 1: Multiply both sides of the equation by \(\displaystyle x\).

\(\displaystyle \rightarrow 5x + 3 = 20x\)

Step 2: Subtract \(\displaystyle 5x\) from both sides of the equation.

\(\displaystyle \rightarrow 3 = 15x\)

Step 3: Divide both sides of the equation by 15.

\(\displaystyle \rightarrow x = \frac{1}{5}\)