\(\displaystyle 4 (x +7) + 2 = 5 (x + 4) - x\)

\(\displaystyle 4 \cdot x +4 \cdot 7 + 2 = 5 \cdot x + 5 \cdot 4 - x\)

\(\displaystyle 4 x +28+ 2 = 5x + 20- x\)

\(\displaystyle 4 x +30 = 4x + 20\)

\(\displaystyle 30 = 20\)

This identically false statement is an indication that there is no solution.

\(\displaystyle 4 (x +9) + 9 = 5 (x + 9) - x\)

\(\displaystyle 4 \cdot x +4 \cdot 9 + 9 = 5 \cdot x + 5 \cdot 9 - x\)

\(\displaystyle 4 x +36 + 9 = 5x + 45 - x\)

\(\displaystyle 4 x + 45 = 4x + 45\)

This identically true statement is an indication that the solution set is the set of all real numbers.

\(\displaystyle 4pk + 9 = S\) 

\(\displaystyle 4pk + 9 -9 = S -9\)

\(\displaystyle 4pk = S -9\)

\(\displaystyle 4pk \div 4k = \left (S -9 \right ) \div 4k\)

\(\displaystyle p = \frac{S-9}{4k}\)

\(\displaystyle 7X -6Y = A\)

\(\displaystyle 7X -6Y + 6Y = A+ 6Y\)

\(\displaystyle 7X = A+ 6Y\)

\(\displaystyle 7X \div 7 = \left (A+ 6Y \right ) \div 7\)

\(\displaystyle X = \frac{A+ 6Y}{7}\)

\(\displaystyle 5X + 6Y = A\)

\(\displaystyle 5X + 6Y - 5X= A- 5X\)

\(\displaystyle 6Y = A- 5X\)

\(\displaystyle 6Y \div 6= \left (A- 5X \right )\div 6\)

\(\displaystyle Y = \frac{A- 5X}{6}\)

Simplify \(\displaystyle 2x+9-x=6x-3x-1\) by combining like terms to get \(\displaystyle x+9=3x-1\). Subtract \(\displaystyle x\) and add \(\displaystyle 1\) to both sides to get \(\displaystyle 10=2x\). Divide both sides by 2 to get \(\displaystyle x=5\).

This equation takes two steps to solve. When solving two steps, first we simplify the addition and subtraction terms. Then we do the multiplication/division step. 

So, in \(\displaystyle 2x-13=9\), our first step is to negate the subtraction of 13. The inverse of subtracting by 13 is to add by 13. So step 1 is to add 13 to both sides. We have

\(\displaystyle 2x-13=9\)

\(\displaystyle +13=+13\)

\(\displaystyle 2x=22\)

From here, we do a second step to solve for \(\displaystyle x\), by doing the inverse of multiplying by 2. The inverse of multiplication is division. So to "get rid" of the 2, we divide both sides by 2. So from,

\(\displaystyle 2x=22 \rightarrow \frac{2x}{2}= \frac{22}{2}\rightarrow x= 11\) 

And that is our answer, \(\displaystyle x=11\).

To solve for \(\displaystyle x\), you must first use the distributive property to simplify the right side of the equation. This gives you \(\displaystyle \ 5x+7=3x+15\).

Then, subtract \(\displaystyle 7\) and \(\displaystyle 3x\) from both sides of the equation to get \(\displaystyle 2x=8\).

Divide both sides by \(\displaystyle 2\) and you will get a solution of \(\displaystyle x=4\).

\(\displaystyle 3x+2=-7\)

First, subtract 2 from both sides.

\(\displaystyle 3x+2-2=-7-2\)

\(\displaystyle 3x=-9\)

Divide both sides by 3.

\(\displaystyle \frac{3x}{3}=\frac{-9}{3}\)

\(\displaystyle x=-3\)

\(\displaystyle 3x+5-5=29-5\)

\(\displaystyle 3x=24\)

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

\(\displaystyle x=8\)