Equations

Help Questions

Algebra II › Equations

Questions 1 - 10

Solve for .

Explanation

Subtract on both sides.

Solve for in the linear equation.

$x = \frac{1}{4}$

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

$x = \frac{1}{3}$

Explanation

To solve for the variable in the linear equation, isolate the variable on one side of the equation with all other constants on the other side. To accomplish this, perform opposite operations when manipulating the equation.

First, add 20x to both sides.

${\color{Red} +20x }$ ${\color{Red} +20x }$

Next subtract 2 from both sides.

${\color{Red} -2 }$ ${\color{Red} -2 }$

Divide both sides by 32.

$\frac{8}{32} = \frac{32x}{32}$

$x = \frac{1}{4}$

Solve for :

$(\frac{1}{2})x +7=15$

Explanation

$(\frac{1}{2})x=15-7=8$

$x=(\frac{2}{1})\times8=16$

Solve for .

Explanation

Subtract on both sides. When adding two negative numbers, we just add the numbers and put a minus sign in the end.

Find the solution to the following equation.

Explanation

Find the solution to the following equation.

To find the solution of this equation, we need to find the value for x, which makes the given equation true.

We do this by working backwards and manipulating the equation.

The easiest first step would probably be to subtract 23 from both sides:

By doing so, we can simplify the equation to get:

Next, simply divide both sides by 9 to get the answer!

$9x\div 9=36\div9$

So we get:

Solve for .

Explanation

In order to solve this equation, we need to isolate the variable, , on the left side of the equals sign. We will do this by performing the same operations on both sides of the equation.

Subtract from both sides of the equation.

Solve.

$\frac{2}{3}x+\frac{2}{3}=-\frac{2}{3}$

$x=-\frac{3}{2}$

$x=\frac{3}{2}$

The answer is not present

Explanation

$\frac{2}{3}x+\frac{2}{3}=-\frac{2}{3}$

Isolate the term with x:

$\frac{2}{3}x=-\frac{2}{3}-\frac{2}{3}$

Simplify:

$\frac{2}{3}x=-\frac{4}{3}$

Isolate x entirely:

$\frac{3}{2}*\frac{2}{3}x=-\frac{4}{3}*\frac{3}{2}$

$\mathbf{x=-2}$

Tom is painting a fence feet long. He starts at the West end of the fence and paints at a rate of feet per hour. After hours, Huck joins Tom and begins painting from the East end of the fence at a rate of feet per hour. After hours of the two boys painting at the same time, Tom leaves Huck to finish the job by himself.

If Huck completes painting the entire fence after Tom leaves, how many more hours will Huck work than Tom?

$6\ hours$

$10\ hours$

$4\ hours$

$3\ hours$

$5\ hours$

Explanation

Tom paints for a total of hours (2 on his own, 2 with Huck's help). Since he paints at a rate of feet per hour, use the formula

$distance = rate \times time$ (or )

to determine the total length of the fence Tom paints.

feet

Subtracting this from the total length of the fence feet gives the length of the fence Tom will NOT paint: feet. If Huck finishes the job, he will paint that feet of the fence. Using , we can determine how long this will take Huck to do: