Ready to try your luck at some GED algebra questions in preparation for the Mathematical Reasoning subject test? Give our GED Math Algebra Practice Test a try to see where you stand (answer key at the end of the post). Then, if you need more review, read up on GED algebra prep.

## GED Math Algebra Practice Test

1. What is the value of x in the following equation?

3x+4=25

A) 3

B) 4

C) 7

D) 10

2. What is the sum of the two polynomials below?

(2x^{2}-x+5)+(3x^{2}+7x-1)

A) 5x^{2}+6x+4

B) -x^{2}-8x+6

C) 5x^{2}-8x+6

D) -x^{2}+6x+4

3. What is the value of x in the following equation?

x-4=23

A) 14

B) 19

C) 23

D) 27

4. Which choice gives the difference of the following two polynomials?

(3x^{2}-2x+6)-(5x^{2}+8x-3)

A) 8x^{2}+6x+3

B) -2x^{2}-10x+9

C) -8x^{2}-6x-3

D) 2x^{2}+10x-9

5. Which choice gives the solution to the following inequality?

-4x-5>31

A) x>-9

B) x>9

C) x<-9

D) x<9

6. Which choice gives the values of x and y in the following system of equations?

x+3y=13

4x-7y=-43

A) x=-5; y=2

B) x=5; y=2

C) x=2; y=5

D) x=-2; y=5

7. Which choice gives the product of the following two binomials?

(3x+4)(4x-3)

A) 12x^{2}+7x-12

B) 12x^{2}-12

C) 12x^{2}+12x-12

D) 12x^{2}-7

8. Which choice gives the solution to the following inequality?

6x+2<26

A) x-4

B) x<4

C) x>-4

D) x<-4

9. Which choice gives the quotient of the following two expressions?

A) 4x

B) 7-3x

C) 10x

D) 7x-3

10. Which choice shows a way to correctly factor the following polynomial?

3x^{5}-51x^{4}+39x^{3}-15x^{2}

A) 3x(1-17+13-5)

B) 3x(x-17x+13x-5x)

C) 3x^{2}(x^{4}-17x^{3}+13x^{2}-5x)

D) 3x^{2}(x^{3}-17x^{2}+13x-5)

### Answer Key

**1. C **

This is a basic two-step equation with 1 variable. You need to use inverse operations to isolate the x on one side of the equation. It requires two steps: 1) subtract 4 from each side of the equation; and 2) divide each side of the equation by 3:

3x+4=25

3x=21

x=7

**2. A **

To find the sum of the two polynomials, you need to complete two steps: 1) rearrange the polynomials by like terms; and 2) combine like terms to simplify:

(2x^{2}-x+5)+(3x^{2}+7x-1)

2x^{2}+3x^{2}-x+7x+5-1

2x^{2}+3x^{2}-x+7x+5-1

5x^{2}-x+7x+5-1

5x^{2}+6x+5-1

5x^{2}+6x+4

**3. D **

This is a basic one-step equation with one variable. You need to use inverse operations to isolate the x on one side of the equation. All this equation requires is to cancel the 4 on the left side by adding it to both sides of the equation:

x-4=23

x=27

**4. B**

To find the difference of the two polynomials, you need complete three steps: 1) reverse each sign in the polynomial you are subtracting; 2) rearrange the polynomials by like terms; and 2) combine like terms to simplify:

(3x^{2}-2x+6)-(5x^{2}+8x-3)

3x^{2}-2x+6-5x^{2}-8x+3

3x^{2}-5x^{2}-2x-8x+6+3

-2x^{2}-2x-8x+6+3

-2x^{2}-10x+6+3

-2x^{2}-10x+9

**5. C **

To solve inequalities, you need to follow the same rules as you would for solving equations, with one exception: when you multiply or divide by a negative number, you must flip the direction of the inequality sign. To solve this inequality, you need to follow three steps: 1) add 5 to both sides of the inequality; 2) divide both sides of the inequality by -4; and 3) flip the greater than sign so that it becomes a less than sign:

-4x-5>31

-4x>36

x<-9

**6. D **

To solve a system of equations, you need to follow five steps: 1) isolate the x in one of the equations to find an expression describing it; 2) substitute the expression of x into the other equation; 3) solve for y; 4) plug the value of y into either equation; and 5) solve for x:

Step 1: Isolate x in either equation. In the first equation, you can accomplish this by subtracting 3y from both sides of the equation.

x+3y=13

x=13-3y

Step 2: Plug the expression of x into the other.

4x-7y=-43

4(13-3y)-7y=-43

Step 3: Solve for y. First use the distributive property to remove the parentheses on the left side of the equation. Then simplify and use inverse operations to isolate y on one side of the equation.

4(13-3y)-7y=-43

52-12y-7y=-43

52-19y=-43

-19y=-95

y=5

Step 4: Plug the value of y into either equation. Think about which equation might be easier to work with. Since the first equation has smaller constants and coefficients, it will likely be easier to calculate the value of x using this equation.

x+3y=13

x+3(5)=13

Step 5: Solve for x. First multiply to remove the parentheses, then subtract 15 from both sides of the equation.

x+3(5)=13

x+15=13

x+15=13

x=-2

You have now found that y=5 and x=-2 using the substitution method for solving a system of equations.

**7. A **

To multiply two binomials, use the FOIL (first, outside, inside, last) method to ensure that each term in the first binomial is multiplied by each term in the second binomial. Then, combine like terms.

Step 1: Multiply the** first** terms in each binomial.

(3x+4)(4x-3)

(3x)(4x)=12x^{2}

Step 2: Multiply the **outside** terms in each binomial.

(3x+4)(4x-3)

(3x)(-3)= -9x

Step 3: Multiply the **inside** terms in each binomial.

(3x+4)(4x-3)

(4)(4x)=16x

Step 4: Multiply the **last** terms in each binomial.

(3x+4)(4x-3)

(4)(-3)=-12

Step 5: Put the products together in one polynomial. Then, combine like terms.

12x^{2}-9x+16x-12

12x^{2}+7x-12

**8. B **

To solve inequalities, you need to follow the same rules as you would for solving equations, with one exception: when you multiply or divide by a negative number, you must flip the direction of the inequality sign. To solve this inequality, you need to follow two steps: 1) subtract 2 from both sides of the inequality; and 2) divide both sides of the inequality by 6. Since you do not need to multiply or divide by a negative number, you should not flip the inequality sign.

6x+2<26

6x<24

x<4

**9. D **

In this instance, since you’re not asked to solve for x, dividing a polynomial by another expression means to simplify the rational expression. The easiest way to do this involves four steps: 1) split the numerator and create two separate fractions; 2) simplify the first fraction; 3) simplify the second fraction; and 4) combine the two simplified expressions.

Step 1: Split the numerator. The two fractions you create will have the same denominator: 4x.

Step 2: Simplify the first fraction. Remember that x^{2}÷x simplifies to x. Simplify the coefficients by dividing them.

Step 3: Simplify the second fraction. The two x variables cancel each other, and so you are left with dividing -12 by 4.

Step 4: Combine the two simplified expressions. Remember that adding a negative number is just like subtracting a number, and so you can simply remove the sign from the equation.

7x-3

**10. D **

To factor a polynomial, you need to follow three steps: 1) find the greatest common factor for each term; 2) pull out the greatest common factor (GCF); and 3) set the remaining factors in parentheses.

It is important to remember that when you multiply two variables, you add their exponents. Conversely, when you divide two variables, you subtract their exponents. From this property of exponents comes the rule that when you pull out a variable as part of the GCF, the exponent of the variable in the remaining factor will go down by the exponent in the GCF. For example, x^{3}=x(x^{2}).Keeping this information in mind, follow the steps below to factor this polynomial:

Step 1: Find the GCF. The coefficient of each term has a factor of 3. The variable of each term has a factor of x^{2}. So, the greatest common factor is 3x^{2}.

Step 2: Pull out the greatest common factor. Show this step by setting 3x outside a set of parentheses:

3x^{2}( )

Step 3: Set the remaining factors inside of the parentheses. To find the remaining factors, divide each term in the polynomial by 3x^{2}.

3x^{2}( x^{3}-17x^{2}+13x-5)