Here are some free algebra questions from our practice tests.

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Arithmetic – Exam Information and Exercises

Algebra – More Example Problems

## Example 1:

Polynomials are algebraic expressions that contain more than one term. You will definitely have questions on the exam about multiplying polynomials.

### Solution 1:

When multiplying polynomials, you should use the F-O-I-L method.

This means that you multiply the variables two at a time from each of the two parts of the equation in the parentheses in this order:

First – Outside – Inside – Last

So, the first variables in each set of parentheses are 2*x* and 2*x*

FIRST:

The variables on the outside of each set of parentheses are 2x and 3y

OUTSIDE:

The variables on the inside of each set of parentheses are -3y and 2x

INSIDE:

The last variables in each set of parentheses are -3*y* and -3*y*

LAST:

Then we add all of the above parts together to get:

## Example 2:

Algebra questions on the Accuplacer Test will also include inequalities problems. Inequalities contain the less than or greater than signs.

31 – ^{2}/_{3}x > 27, then x < ?

### Solution 2:

In order to solve inequalities, deal with the whole numbers on each side of the equation first:

31 – ^{2}/_{3}x > 27

(31 – 31) – ^{2}/_{3}x > (27 – 31)

–^{2}/_{3}x > -4

Then deal with the fraction:

–^{2}/_{3}x > -4

3 × –^{2}/_{3}x > -4 × 3

-2x > -12

Then deal with the remaining whole numbers:

-2x > -12

-2x ÷ 2 > -12 ÷ 2

-x > -6

Then, deal with the negative number:

-x > -6

-x + 6 > -6 + 6

-x + 6 > 0

Finally, isolate the unknown variable as a positive number:

-x + 6 > 0

– x + x + 6 > 0 + x

6 > x

x < 6

Continue studying with the problems for Advanced Algebra and Geometry.