To solve for  we must get all of the constants on the other side of the equation as .

To do this in a problem where  is being subtracted by a number, we must add the number to both sides of the equation.

In this case the number is $\displaystyle \frac{7}{5}$ so we add $\displaystyle \frac{7}{5}$ to each side of the equation: $\displaystyle x-\frac{7}{5}+\frac{7}{5}=\frac{5}{8}+\frac{7}{5}$

To add fractions we must first ensure that we have the same denominator.

To do this we must find the least common multiple of the denominators.

In this case the LCM is $\displaystyle 40$.

We then multiply $\displaystyle \frac{5}{8}*\frac{5}{5}$ and $\displaystyle \frac{7}{5}*\frac{8}{8}$ to get the same denominator for both fractions.

To multiply a fraction, multiply the top number of the first fraction by the top number of the second fraction and the bottom number of the first fraction by the bottom number of the second fraction.

 $\displaystyle x=\frac{25}{40}+\frac{56}{40}$

We then add the numerators together and place the result over the new denominator.

 $\displaystyle x=\frac{81}{40}$

Our goal here is to isolate $\displaystyle x$. That means we want just $\displaystyle x$ on the left side.

For our problem, $\displaystyle \frac{2}{7}x=18$, we need to get rid of the fraction. Dividing by a fraction is the same as multiplying by the reciprocal.

$\displaystyle \frac{2}{7}x=18$

$\displaystyle \frac{7}{2}*\frac{2}{7}x=18*\frac{7}{2}$

$\displaystyle \frac{14}{14}x=\frac{18*7}{2}$

$\displaystyle x=\frac{126}{2}$

$\displaystyle x=63$

When solving for $\displaystyle x$, we want to isolate it. That means we want only $\displaystyle x$ on the right side of the equation.

For our given equation, $\displaystyle 32=\frac{1}2{}x$, we need to divide both sides by $\displaystyle \frac{1}{2}$.

Dividing by a fraction is the same as multiplying by the reciprocal so this will look like:

$\displaystyle \frac{2}{1}*32=\frac{1}2{}x*\frac{2}{1}$

$\displaystyle \frac{2}{1}*\frac{32}{1}=\frac{1}2{}x*\frac{2}{1}$

$\displaystyle \frac{2*32}{1}=\frac{1*2}{2*1}x$

$\displaystyle \frac{64}{1}=\frac{2}{2}x$

$\displaystyle 64=x$

$\displaystyle x=4*\frac{1}{2}$

$\displaystyle x=\frac{4}{1}*\frac{1}{2}$

$\displaystyle x=\frac{4*1}{1*2}$

$\displaystyle x=\frac{4}{2}$

$\displaystyle x=2$

$\displaystyle x=20*\frac{3}{2}$

$\displaystyle x=\frac{20}{1}*\frac{3}{2}$

$\displaystyle x=\frac{20*3}{1*2}$

$\displaystyle x=\frac{60}{2}$

$\displaystyle x=30$

For this problem, multiply across on the right side:

$\displaystyle x=5*\frac{1}{5}$

$\displaystyle x=\frac{5}{1}*\frac{1}{5}=\frac{5}{5}=1$

To solve this problem, multiply across on the right side:

$\displaystyle x=12*\frac{1}{3}=\frac{12}{1}*\frac{1}{3}=\frac{12}{3}=4$

To divide both sides by a fraction, we multiply both sides by the reciprocal. 

$\displaystyle \frac{3}{2}*\frac{2}{3}x=8*\frac{3}{2}$

$\displaystyle \frac{3*2}{2*3}x=\frac{8*3}{2}$

$\displaystyle \frac{6}{6}x=\frac{24}{2}$

$\displaystyle x=\frac{24}{2}$

$\displaystyle x=12$

To solve for  we must get all of the numbers on the other side of the equation as .

To do this in a problem where a number is being added to , we must subtract the number from both sides of the equation.

In this case the number is $\displaystyle .12$ so we subtract $\displaystyle .12$ from each side of the equation to make it look like this $\displaystyle x+.12-.12=.15-.12$

The numbers on the left side cancel to leave  by itself.

To do the necessary subtraction we need to know how to subtract decimals from each other.

To subtract decimals you place the first decimal over the top of the other aligned by the decimal point. 

Then go through each place and subtract the top number by the bottom number.

Subtract the numbers in each place like you would any number $\displaystyle 5-2=3$ and $\displaystyle 1-1=0$

Combine the numbers and keep the decimal in the same place to get $\displaystyle .15-.12=.03$

The answer is $\displaystyle x=.03$

To solve for $\displaystyle x$ we must get all of the numbers on the other side of the equation of $\displaystyle x$.

To do this in a problem where $\displaystyle x$ is being multiplied by a number, we must divide both sides of the equation by the number.

In this case the number is $\displaystyle .03$ so we divide each side of the equation by $\displaystyle .03$ to make it look like this $\displaystyle \frac{.03x}{.03}=\frac{.09}{.03}$

Then we must divide the decimals by each other to find the answer.

To divide decimals we line the decimals up like this $\displaystyle \frac{.09}{.03}$.

Then ignoring all of the decimal places we divide the top number by the bottom number to get $\displaystyle \frac{9}{3}=3$

Then we must apply the decimals.

However many decimal places there are in the denominator will be subtracted from the number of decimal places in the numerator to get the final number of decimal places in our answer.

If the number is positive we move the decimal that number of places to the left of our number.

If the number is negative we move the decimal that number of places to the right of our number.

In this case it would be $\displaystyle 2-2=0$ so we don't have any decimal places and the answer is  $\displaystyle 3$.