This equation can be solved in three steps.

First, subtract \(\displaystyle 9\) from both sides of the equation to isolate the variable and its coefficient on the left side of the equation.

\(\displaystyle \frac{12}{x} + 9 = 13\)

\(\displaystyle \rightarrow (\frac{12}{x} + 9) - 9 = (13) - 9\)

\(\displaystyle \rightarrow \frac{12}{x} = 4\)

Now multiply both sides by \(\displaystyle x\) since \(\displaystyle x\) cannot be solved for while it is in the denominator.

\(\displaystyle (\frac{12}{x}) \times x = (4) \times x\)

\(\displaystyle \rightarrow 12 = 4x\)

Finally, divide both sides by \(\displaystyle 4\) to isolate \(\displaystyle x\) and find the solution.

\(\displaystyle \frac{(12)}{4} = \frac{(4x)}{4}\)

\(\displaystyle \rightarrow 3 = x\)

\(\displaystyle \frac{12}{a}-7=-1\)

Add 7 to both sides.

\(\displaystyle \frac{12}{a}-7+7=-1+7\)

\(\displaystyle \frac{12}{a}=6\)

Multiply both sides by \(\displaystyle \small a\).

\(\displaystyle \frac{12}{a}(a)=6a\)

\(\displaystyle 12=6a\)

Divide both sides by 6.

\(\displaystyle \frac{12}{6}=\frac{6a}{6}\)

\(\displaystyle 2=a\)

\(\displaystyle (2x\div4) +5 = 25\)

We need to isolate \(\displaystyle \small x\). First, subtract \(\displaystyle \small 5\) from both sides.

\(\displaystyle (2x\div4) +5-5 = 25-5\)

\(\displaystyle (2x\div4) = 20\)

Multiply both sides by \(\displaystyle \small 4\).

\(\displaystyle 2x\div4 *4= 20*4\)

\(\displaystyle 2x=80\)

Finally, divide both sides by \(\displaystyle \small 2\).

\(\displaystyle \frac{2x}{2}=\frac{80}{2}\)

\(\displaystyle x=40\)

\(\displaystyle \frac{a}{4}+3=12\)

We need to work to isolate the variable using inverse functions.

Subtract \(\displaystyle \small 3\) from both sides.
\(\displaystyle \frac{a}{4}+3-3=12-3\)

\(\displaystyle \frac{a}{4}=9\)

Multiply both sides by \(\displaystyle \small 4\).

\(\displaystyle (4)\frac{a}{4}=(4)(9)\)

\(\displaystyle a=36\)

\(\displaystyle x=\frac{2}{3}*18\)

From here, you can either plug this into your calculator, or take the equation in pieces: 

\(\displaystyle x=\frac{2*18}{3}\)

\(\displaystyle x=\frac{36}{3}\)

\(\displaystyle x=12\)

To solve \(\displaystyle \frac{2}{3}*(x+5)=12\), first we need to get rid of the fraction. Dividing by a fraction is the same as multiplying by a reciprocal, so multiply both sides by \(\displaystyle \frac{3}{2}\).

\(\displaystyle \frac{2}{3}*(x+5)=12\)

\(\displaystyle \frac{3}{2}*\frac{2}{3}*(x+5)=12*\frac{3}{2}\)

\(\displaystyle x+5=12*\frac{3}{2}\)

\(\displaystyle x+5=\frac{12*3}{2}\)

\(\displaystyle x+5=\frac{36}{2}\)

\(\displaystyle x+5=18\)

Subtract \(\displaystyle 5\) from both sides.

\(\displaystyle x+5-5=18-5\)

\(\displaystyle x=18-5\)

\(\displaystyle x=13\)

To solve \(\displaystyle \frac{2}{3}x=10\), we need to get rid of the fraction. To do that, we multiply both sides by the reciprocal of that fraction.

\(\displaystyle \frac{3}{2}*\frac{2}{3}x=10*\frac{3}{2}\)

\(\displaystyle x=10*\frac{3}{2}\)

From here, you can either plug that fraction into your calculator or solve in pieces.

\(\displaystyle x=\frac{10*3}{2}\)

\(\displaystyle x=\frac{30}{2}\)

\(\displaystyle x=15\)

To solve for \(\displaystyle x\), we need to isolate our variable. That means that we want ONLY the \(\displaystyle x\) on the left side of the equation.

First, combine our like terms on the right side.

\(\displaystyle \frac{3}{4}x=118+2\)

\(\displaystyle \frac{3}{4}x=120\)

Now divide both sides by \(\displaystyle \frac{3}{4}\). Remember, dividing by a fraction is the same as multiplying by the reciprocal, so we're going to multiply both sides by \(\displaystyle \frac{4}{3}\).

\(\displaystyle \frac{3}{4}x*\frac{4}{3}=120*\frac{4}{3}\)

Since \(\displaystyle \frac{3}{4}*\frac{4}{3}=\frac{12}{12}=1\), we can ignore it.

\(\displaystyle x=\frac{120}{1}*\frac{4}{3}\)

\(\displaystyle x=\frac{480}{3}\)

\(\displaystyle x=160\)

First, find the total number of marbles in the glass jar: \(\displaystyle 100 + 75 + 25 = 200\) marbles in total.

It is given that there are 75 red marbles, thus: \(\displaystyle 75/200 = 3/8\).

First add 9 to both sides:

\(\displaystyle 15+(9)=\frac{Y}{3}-9+(9)\)

\(\displaystyle 24=\frac{Y}{3}\)

Then multiply both sides by 3:

\(\displaystyle 24\left ( 3\right )=\frac{Y}{3}\left ( 3\right )\)

\(\displaystyle 72=Y\)