Basic Single-Variable Algebra

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Math › Basic Single-Variable Algebra

Questions 1 - 10

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.

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

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

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

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:

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

$\mathbf{x=-2}$

Set up the equation: Nine more than three times the cube of a number is four.

Explanation

Split the sentence into parts.

The cube of a number:

Three times the cube of a number:

Nine more than three times the cube of a number:

Is four:

Combine the parts to form the equation.

The answer is:

A circular tower stands surrounded by a circular moat. A bridge provides a passage over the moat to the tower. The distance from the outer edge of the moat to the center of the tower is meters. The area of the floor of tower is $4900\pi$ $m^{2}$ . How long is the bridge over the moat?

Explanation

The distance from the outer edge of the moat to the center of the castle is the radius (100 m) of the larger circle formed by the outer edge of the circular moat.

The radius of the tower's floor (found using the area of the floor), needs to be subracted from 100 m to find the distance fo the bridge.

$\sqrt{4900}=70$

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:

hours.

If Huck works hours and Tom works hours, he works more hours than Tom.

x varies inversely with y. When x=10, y=6. When x=3, what is y?

Explanation

Inverse variation takes the form:

$y=\frac{k}{x}$

Plugging in:

$6=\frac{k}{10}$

Then solve when x=3:

Set up the equation: Nine more than three times the cube of a number is four.

Explanation

Split the sentence into parts.

The cube of a number:

Three times the cube of a number:

Nine more than three times the cube of a number:

Is four:

Combine the parts to form the equation.

The answer is:

The distance of a cyclist is directly proportional to the time he has traveled. Suppose he has traveled 12 miles in 1.5 hours. How far does he travel in a half hour?