Algebra Practice Problems and Answers
Here are some free practice algebra problems and answers to help you study. Go to the links at the bottom of the page for more problems.
1) Expand the following:
2) 31 – 2/3x > 27, then x < ?
3) Factor using the greatest common factor: 4a2 + 16ab + 24b4 – 8
4) If 5a + 3b = c, then a = ?
5) Solve for x: 10 – 3x = 5x + 2
6) What is the value of the following expression when x = 2 and y = −2 ?
7) −3(7 − 2) − 4(3 − 4) = ?
Answers to the Algebra Practice Problems
1) You need to use the FOIL method to get the answer below.
2) x < 6
3) 4(a2 + 4ab + 6b4 – 2)
4) a = c – 3b/5
5) x = 1
6) −8
7) −11
Solutions to the Algebra Problems
Solutions and explanations for each of the answers to the algebra practice problems are provided in this section.
Solution 1:
Polynomials are algebraic expressions that contain more than one term.
You will definitely have questions on your algebra exam about multiplying polynomials.
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 2x and 2x
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 -3y and -3y
LAST:
Then we add all of the above parts together to get:
Solution 2:
Algebra practice problems usually include inequalities problems and answers. Inequalities contain the less than or greater than signs.
In order to solve inequalities, deal with the whole numbers on each side of the equation first:
31 – 2/3x > 27
(31 – 31) – 2/3x > (27 – 31)
–2/3x > -4
Then deal with the fraction:
–2/3x > -4
3 × –2/3x > -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
Solution 3:
To find the greatest common factor for these kinds of algebra practice problems, isolate all of the integers:
4, 16, 14, 8
Greatest Common Factor
Determine what number can be divided into all of the integers.
Here, all of the integers are divisible by 4.
So the greatest common factor is 4.
Perform the operations as shown:
4a2 + 16ab + 24b4 – 8 =
(4 × a2) + (4 × 4 × ab) + (4 × 6 × b4) + (4 × –2) =
4[(4 × a2) + (4 × 4 × ab) + (4 × 6 × b4) + (4 × –2)] =
4(a2 + 4ab + 6b4 – 2)
Solution 4:
Isolate variable a by performing the operations shown below:
5a + 3b = c
5a + 3b – 3b = c – 3b
a + 3b – 3b = c – 3b
5a = c – 3b
5 × a = c – 3b
5 ÷ 5 × a = c – 3b ÷ 5
5 ÷ 5 × a = c – 3b ÷ 5
a = c – 3b ÷ 5
a = c – 3b/5
Solution 5:
Isolate x first of all.
10 – 3x = 5x + 2
10 – 2 – 3x = 5x + 2 – 2
10 – 2 – 3x = 5x + 2 – 2
8 – 3x = 5x
Then get the variable on only one side of the equation.
8 – 3x = 5x
8 – 3x + 3x = 5x + 3x
8 = 8x
8 = 8 × x
8 = 8 × 1
x = 1
Solution 6:
To solve this problem, put in the values for x and y and multiply.
(2 × 2 × 2) + (3 × 2 × − 2) − (−2 × − 2) =
(2 × 4) + (3 × − 4) − (4) =
8 + (−12) − 4 =
8 − 12 − 4 =
−8
Solution 7:
Perform the operations inside the parentheses.
−3(7 − 2) − 4(3 − 4) =
−3(5) − 4(−1) =
Then multiply to solve.
(−3 × 5) − (4 × −1) =
−15 − (−4) =
−15 + 4 = −11
Algebra Question Types and Tips
We hope these algebra practice problems and answers have helped you.
The algebra questions on your examination will usually include three main types of problems.
Substituting Values
Performing operations with algebraic expressions and formulas, like in this example.
What is the value of the following expression when x = 2 and y = −2 ?
In these algebra practice problems, you need to substitute for x and y and answer.
Rational Numbers & Radicals
There will also be computations on equations with integers, rational numbers, and radicals.
Integers are whole numbers. In other words, they are not fractions or decimals.
You may have to simplify an equation that contains only integers.
Tips:
Two negative signs together make a positive.
Complete the operations inside the parentheses first.
Remember to be careful when multiplying the negative numbers.
Equations, Inequalities & Practical Problems
Problems on solving equations, inequalities, and practical problems like those provided at the first link below
More Algebra Practice Problems and Answers
Get more algebra practice problems and answers with Khan Academy.
Khan Academic – Algebra Problems
Test.com is also a great resource for algebra problems.
All of their algebra practice problems come with explanations and answers, and the problems are organized by skill area.
Try Exam SAM’s free algebra practice problems and answers
50 Free Accuplacer Algebra Problems
More Algebra Practice
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