This is a two-step equation.  First simplify the whole numbers by adding 6 to both sides:

\(\displaystyle 24+\left ( 6\right )=2X-6+\left ( 6\right )\)

\(\displaystyle 30=2X\)

Then divide both sides by 2

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

\(\displaystyle 15=X\)

Perform the same operation on both sides of the equation.

\(\displaystyle 4x-3=13\)

Add 3 to both sides.

\(\displaystyle 4x-3+3=13+3\)

\(\displaystyle 4x=16\)

Divide both sides by 4 and simplify the fraction.

\(\displaystyle \frac{4x}{4}=\frac{16}{4}\)

\(\displaystyle x=4\)

\(\displaystyle 3m + 5 = 17\)

To solve a two step equation, we want to isolate the variable. This means first "getting rid of" the number which is being added to the variable, in this case \(\displaystyle 5\). To get rid of the \(\displaystyle 5\), we first recognize that it is being added, then we do the inverse and subtract \(\displaystyle 5\) from both sides.

\(\displaystyle 3m+5-5=17-5\)

\(\displaystyle 3m=12\)

Now, we want to do the inverse of multiplying by \(\displaystyle 3\), which is dividing by \(\displaystyle 3\) on both sides.

\(\displaystyle \frac{3m}{3}=\frac{12}{3}\)

\(\displaystyle m=4\)

\(\displaystyle 8 - \frac{k}{7} = 5\)

We want to first isolate the variable, thus we first try to get rid of the constants being added to the variable, in this case the \(\displaystyle 8\). To eliminate \(\displaystyle 8\), we do the inverse of addition, and subtract \(\displaystyle 8\) from both sides.

\(\displaystyle 8-\frac{k}{7}-8=5-8\)

\(\displaystyle - \frac{k}{7} = -3\)

Then, we want to do the inverse of dividing by \(\displaystyle -7\), which is multiplying by \(\displaystyle -7\). Remember that multiplying two negative terms results in a positive term.

\(\displaystyle (-7)(-\frac{k}{7})=(-7)(-3)\)

\(\displaystyle k=21\)

\(\displaystyle \small 7p+3=10p\)

Subtract \(\displaystyle 7p\) from both sides to get the variables on the same side, and simplify.

\(\displaystyle \small 7p+3-7p=10p-7p\)

\(\displaystyle \small 3=3p\)

Divide both sides by \(\displaystyle 3\).

\(\displaystyle \small \frac{3}{3}=\frac{3p}{3}\)

\(\displaystyle \small 1=p\)

We have two steps to this problem. Remember our end result is to get \(\displaystyle x\) isolated on one side of the equation.

First we add \(\displaystyle 2\) to each side, cancelling out the \(\displaystyle 2\) on the left side. This brings the equation to \(\displaystyle 4x =16\).

Remember to get rid of a number we perform the opposite operation. The \(\displaystyle 4\) is multiplied with the \(\displaystyle x\), therefore to cancel it out we will divide by \(\displaystyle 4\).

\(\displaystyle 4x\) divided by \(\displaystyle 4\) equals \(\displaystyle x\). What we do to one side we must do to the other, therefore we divide \(\displaystyle 16\) by \(\displaystyle 4\) also. This becomes \(\displaystyle x=4\).

The requires the FOIL method (first, outside, inside, last).

Multiplying the first two monomials \(\displaystyle 2x^2 \cdot 3x^3\) equals \(\displaystyle 6x^{5}\).

The outside two are \(\displaystyle 2x^{2} \cdot 3\) which equals \(\displaystyle 6x^{2}\).

The two inside monomials are \(\displaystyle 5 \cdot 3x^3\) which equals \(\displaystyle 15x^3\).

The last two are \(\displaystyle 5\cdot 3\) which is \(\displaystyle 15\).

All together this becomes \(\displaystyle 6x^{5}+15x^{3}+6x^{2}+15\). 

According to the laws of exponents, if you add you do not add the exponents. Therefore \(\displaystyle 5 +2 =7\), and the variable term remains \(\displaystyle x^{5}\). The answer is \(\displaystyle 7x^5\).

\(\displaystyle 26-s=13\)

Add \(\displaystyle \small s\) to both sides.

\(\displaystyle 26-s+s=13+s\)

\(\displaystyle 26=13+s\)

Subtract 13 from both sides.

\(\displaystyle 26-13=13+s-13\)

\(\displaystyle 13=s\)

\(\displaystyle 6n+14=38\)

Subtract 14 from each side.

\(\displaystyle 6n+14-14=38-14\)

\(\displaystyle 6n=24\)

Divide both sides by 6.

\(\displaystyle \frac{6n}{6}=\frac{24}{6}\)

\(\displaystyle n=4\)