To isolate the variable in the equation, perform the opposite operation to move all constants on one side of the equation and leaving the variable on the other side of the equation.

$\displaystyle \frac{x}{8}-5=-2$ 

Add $\displaystyle 5$ on both sides. Since $\displaystyle 5$ is greater than $\displaystyle 2$ and is positive, our answer is positive. We treat as a normal subtraction.

$\displaystyle \frac{x}{8}=3$ 

Multiply $\displaystyle 8$ on both sides.

$\displaystyle x=24$

To isolate the variable in the equation, perform the opposite operation to move all constants on one side of the equation and leaving the variable on the other side of the equation.

$\displaystyle \frac{x}{-4}-3=-15$ 

Add $\displaystyle 3$ to both sides. Since $\displaystyle 15$ is greater than $\displaystyle 3$ and is negative, our answer is negative. We treat as a normal subtraction.

$\displaystyle \frac{x}{-4}=-12$ 

When multiplying with another negative number, our answer is positive.

$\displaystyle x=48$

To isolate the variable in the equation, perform the opposite operation to move all constants on one side of the equation and leaving the variable on the other side of the equation.

$\displaystyle \sqrt{x}=25$ 

To get rid of the radical, we square both sides.

$\displaystyle x=25^2=625$

To isolate the variable in the equation, perform the opposite operation to move all constants on one side of the equation and leaving the variable on the other side of the equation.

$\displaystyle \sqrt{x+3}=16$ 

To get rid of the radical, we square both sides.

$\displaystyle x+3=16^2=256$ 

Subtract $\displaystyle 3$ on both sides.

$\displaystyle x=253$

To isolate the variable in the equation, perform the opposite operation to move all constants on one side of the equation and leaving the variable on the other side of the equation.

$\displaystyle x^2=361$ 

Take the square root on both sides.  Remember when you do that, you need to take account of the negative as well. Two negatives multipied is a positive number.

$\displaystyle x=\pm \sqrt{361}=\pm19$

To isolate the variable in the equation, perform the opposite operation to move all constants on one side of the equation and leaving the variable on the other side of the equation.

$\displaystyle x^2+6x+8=0$ 

This is a quadratic equation. We need to find two terms that are factors of the c term that add up to the b term.

In this case, we should have $\displaystyle (x+2)(x+4)=0$. 

Solve each binomial individually. 

$\displaystyle x+2=0$ Subtract $\displaystyle 2$ on both sides. $\displaystyle x=-2$

$\displaystyle x+4=0$ Subtract $\displaystyle 4$ on both sides. $\displaystyle x=-4$

Answers are $\displaystyle -2, -4$.

$\displaystyle x+24=103$ Subtract $\displaystyle 24$ on both sides.

$\displaystyle x=79$

$\displaystyle x+46=21$ Subtract $\displaystyle 46$ on both sides. Since $\displaystyle 46$ is greater than $\displaystyle 21$ and is negative, our answer is negative. We treat as a normal subtraction.

$\displaystyle x=-25$

$\displaystyle x-85=213$ Add $\displaystyle 85$ to both sides.

$\displaystyle x=298$

$\displaystyle x-145=-241$ Add $\displaystyle 145$ on both sides. Since $\displaystyle 241$ is greater than $\displaystyle 145$ and is negative, our answer is negative. We treat as a normal subtraction.

$\displaystyle x=-96$