First, subtract \(\displaystyle 425\) from both sides of the equation:

\(\displaystyle 25x + 425 = 787.5\)

\(\displaystyle 25x = 362.5\)

Then, divide both sides by \(\displaystyle 25\) to solve for \(\displaystyle x\):

\(\displaystyle 362.5 \div 25 = 14.5\)

\(\displaystyle x = 14.5\)

In order to solve this equation, we have to isolate the variable \(\displaystyle x\) on the left side of the equals sign. We will do this by performing the same operations to both sides of the equation:

\(\displaystyle 2x-9=-5\)

Add \(\displaystyle 9\) to both sides of the equation. 

\(\displaystyle 2x-9+9=-5+9\)

Remember that adding a negative number to a positive number is the same as subtracting a positive number.

\(\displaystyle 2x=9-5\)

\(\displaystyle 2x=4\)

Divide both sides of the equation by \(\displaystyle 2\).

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

Simplify.

\(\displaystyle x=2\)

In order to solve this equation, we have to isolate the variable \(\displaystyle x\) on the left side of the equals sign. We will do this by performing the same operations to both sides of the equation:

\(\displaystyle 4x+10=34\)

Subtract \(\displaystyle 10\) from both sides of the eqaution.

\(\displaystyle 4x+10-10=34-10\)

\(\displaystyle 4x=24\)

Divide both sides of the equation by \(\displaystyle 4\).

\(\displaystyle \frac{4x}{4}=\frac{24}{4}\)

Simplify.

\(\displaystyle x=6\)

In order to solve this equation, we have to isolate the variable \(\displaystyle x\) on the left side of the equals sign. We will do this by performing the same operations to both sides of the equation:

\(\displaystyle \frac{1}{3}x-2=\frac{2}{3}\)

Add \(\displaystyle 2\) to both sides of the equation.

\(\displaystyle \frac{1}{3}x-2+2=\frac{2}{3}+2\)

Simplify the left side and find a common denominator to add the fractions on the right side of the equation.

\(\displaystyle \frac{1}{3}x=\frac{2}{3}+\frac{6}{3}\)

Simplify.

\(\displaystyle \frac{1}{3}x=\frac{8}{3}\)

Multiply both sides  of the equation by \(\displaystyle 3\).

\(\displaystyle \frac{3}{1}\times \frac{1}{3}x=\frac{8}{3} \times \frac{3}{1}\)

Simplify.

\(\displaystyle x=8\)

In order to solve this equation, we have to isolate the variable \(\displaystyle x\) on the left side of the equals sign. We will do this by performing the same operations to both sides of the equation:

\(\displaystyle 5x-1=12\)

Add \(\displaystyle 1\) to both sides of the equation.

\(\displaystyle 5x-1+1=12+1\)

\(\displaystyle 5x=13\)

Divide both sides of the equation by \(\displaystyle 5\).

\(\displaystyle \frac{5x}{5}=\frac{13}{5}\)

Simplify.

\(\displaystyle x=\frac{13}{5}\)

In order to solve this equation, we have to isolate the variable \(\displaystyle x\) on the left side of the equals sign. We will do this by performing the same operations to both sides of the equation:

\(\displaystyle -2x-2=16\)

Add \(\displaystyle 2\) to both sides of the equation.

\(\displaystyle -2x-2+2=16+2\)

\(\displaystyle -2x=18\)

Divide both sides of the equation by \(\displaystyle -2\).

\(\displaystyle \frac{-2x}{-2}=\frac{18}{-2}\)

Remember that when a positive number is divided by a negative number, the answer is always negative.

\(\displaystyle x=-\frac{18}{2}\)

Simplify.

\(\displaystyle x=-9\)

In order to solve this equation, we have to isolate the variable \(\displaystyle x\) on the left side of the equals sign. We will do this by performing the same operations to both sides of the equation:

\(\displaystyle 12-3x=0\)

Subtract \(\displaystyle 12\) from both sides of the equation.

\(\displaystyle 12-12-3x=0-12\)

\(\displaystyle -3x=-12\)

Divide both sides of the equation by \(\displaystyle -3\).

\(\displaystyle \frac{-3x}{-3}=\frac{-12}{-3}\)

Simplify. Remember that when a negative number is divided by a negative number, the answer is always positive.

\(\displaystyle x=4\)

In order to solve this equation, we have to isolate the variable \(\displaystyle x\) on the left side of the equals sign. We will do this by performing the same operations to both sides of the equation:

\(\displaystyle -9x=-900\)

Divide both sides by \(\displaystyle -9\).

\(\displaystyle \frac{-9x}{-9}=\frac{-900}{-9}\)

Simplify. Remember that when a negative number is divided by a negative number, the answer is always positive.

\(\displaystyle x=100\)

In order to solve for \(\displaystyle x\), we need to isolate it on the left side of the equation. We will do this by performing the same operations to both sides of the given equation:

\(\displaystyle 3x+5=41\) 

Subtract \(\displaystyle 5\) from both sides of the equation.

\(\displaystyle 3x+5-5=41-5\)

Simplify. 

\(\displaystyle 3x=36\)  

Divide both sides of the equation by \(\displaystyle 3\). 

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

Solve.

\(\displaystyle x=12\)

In order to solve for \(\displaystyle x\), we need to isolate it on the left side of the equation. We will do this by performing the same operations to both sides of the given equation:

\(\displaystyle 4x+16=-20\) 

Subtract \(\displaystyle -16\) from both sides of the equation.

\(\displaystyle 4x+16-16=-20-16\)

When subtracting a negative number from another negative number, we will treat it as an addition problem and then add a negative sign to the sum.

\(\displaystyle 4x=-(20+16)\)

Simplify.

\(\displaystyle 4x=-36\) 

Divide both sides of the equation by \(\displaystyle 4\). 

\(\displaystyle \frac{4x}{4}=\frac{-36}{4}\)

Solve. When dividing a negative number by a positive number, our answer becomes negative.

\(\displaystyle x=-9\)