There are TWO ways:

Method \(\displaystyle 1\): (not so preferred)

\(\displaystyle \frac{2}{3}(x+3)=24\) Distribute \(\displaystyle \frac{2}{3}\).

\(\displaystyle \frac{2x}{3}+2=24\) Subtract \(\displaystyle 2\) on both sides.

\(\displaystyle \frac{2x}{3}=22\) Multiply \(\displaystyle \frac{3}{2}\) on both sides.

\(\displaystyle x=33\)

Method \(\displaystyle 2\): (preferred)

\(\displaystyle \frac{2}{3}(x+3)=24\) Multiply \(\displaystyle \frac{3}{2}\) on both sides.

\(\displaystyle x+3=36\) Subtract \(\displaystyle 3\) on both sides.

\(\displaystyle x=33\)

\(\displaystyle \frac{2}{3}=\frac{x}{12}\) Cross-multiply.

\(\displaystyle 3x=24\) Divide \(\displaystyle 3\) on both sides.

\(\displaystyle x=8\)

\(\displaystyle \frac{4}{x+12}=\frac{10}{85}\) Cross-multiply. Remember the \(\displaystyle 10\) multiplies the whole expression.

\(\displaystyle 10(x+12)=4*85\) Distribute.

\(\displaystyle 10x+120=340\) Subtract \(\displaystyle 120\) on both sides.

\(\displaystyle 10x=220\) Divide \(\displaystyle 10\) on both sides.

\(\displaystyle x=22\)

Solve \(\displaystyle 2x+5=7\) by:

The objective is to solve the equation to find what \(\displaystyle x\) is equal to, so we need to have \(\displaystyle x=\) a value.

First subtract 5 from both sides , and we will get:

\(\displaystyle 2x=2\)

Divide both sides by 2 and the solution is:

\(\displaystyle x=1\)

The objective is to solve the equation to find what \(\displaystyle x\) is equal to, so we need to have \(\displaystyle x=\) a value.

\(\displaystyle 4x+18=2x-4\)

1. Subtract \(\displaystyle 2x\) from both sides, and we will have:

\(\displaystyle 2x+18=-4\)

2. Subtract 18 from both sides, and we will have:

\(\displaystyle 2x=-22\)

3. Divide both sides of the equation by 2 and the solution is:

\(\displaystyle x=-11\)

To solve:

\(\displaystyle 5x + 14 -2(x+4)=x+3(x+1)-(x-3)\)

1. First clear the parentheses.

\(\displaystyle 5x + 14 -2x-8=x+3x+3-x+3\)

2. Add the variables.

\(\displaystyle 3x+ 14-8=3x+3+3\)

3. Add the integers.

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

4. Subtract \(\displaystyle 3x\) from each side.

\(\displaystyle 6=6\)

Which is always true, so x can be all real numbers.

To simplify this you need to isolate x by subtracting 64 from both sides then taking the square root to get:

\(\displaystyle \small \sqrt{-100}\)

you cannot take the square root of a negative number so you answer is no solution.

This is a simple two step problem in which you need to isolate "x" The first step is to subtract the 36 from both sides. Upon doing this you get:

\(\displaystyle \small -12x=60\)

The next step is to divide by -12 to get "x" by itself.

Your final answer is:

\(\displaystyle \small x=-5\)

\(\displaystyle 3x - 2 = \frac{x}{4}\)

We can start by multiplying both sides by the denominator \(\displaystyle 4\)

\(\displaystyle 4\times (3x-2)=4\times \frac{x}{4}\)

\(\displaystyle 12x - 8 = x\)

Isolate terms with \(\displaystyle x\) on one side of the equation, 

\(\displaystyle 12x -x = 8\)

Collect terms and solve, 

\(\displaystyle 11x = 8\)

\(\displaystyle x = \frac{8}{11}\)

Step 1: Cross multiply

\(\displaystyle (a-7)(a-3)=(a-9)(a+3)\)

Step 2: FOIL the polynomials

\(\displaystyle a^2-10a+21=a^2-6a-27\)

Step 3: Combine like terms & solve

\(\displaystyle 48=4a\)

\(\displaystyle 12=a\)