GED practice test

GED Algebraic Problem Solving Practice Test

Expressions, linear equations and inequalities, systems, slope, functions, quadratics and exponents. 55% of Math. Here are 10 GED algebraic problem solving questions, each with the answer and the reason.

Updated 2026-11-14 by the Tigertest team. Based on the assessment targets in the GED Testing Service Assessment Guide for Educators (October 2020 edition). Original questions; not affiliated with GED Testing Service.

1. 1.

   What value of $x$ makes the equation $7 - 2x = 15$ true?

   • A.

     $4$

   • B.

     $-4$

   • C.

     $11$

   • D.

     $-11$

   Answer: B.

   Subtract 7 from both sides: $-2x = 8$. Divide by $-2$: $x = -4$. Dropping the negative sign gives 4, and adding 7 instead of subtracting gives $-11$.

2. 2.

   What value of $x$ makes the equation $4(x + 3) = 2x - 6$ true?

   • A.

     $-3$

   • B.

     $9$

   • C.

     $-9$

   • D.

     $-4.5$

   Answer: C.

   Distribute: $4x + 12 = 2x - 6$. Subtract $2x$: $2x + 12 = -6$. Subtract 12: $2x = -18$, so $x = -9$. Distributing the 4 to only the $x$ gives $4x + 3 = 2x - 6$ and $x = -4.5$; a sign slip gives $x = 9$ or $x = -3$.

3. 3.

   Which inequality describes all solutions of $\frac{x}{2} - 1 < 4$?

   • A.

     $x < 6$

   • B.

     $x > 10$

   • C.

     $x < 2.5$

   • D.

     $x < 10$

   Answer: D.

   Add 1 to both sides: $\frac{x}{2} < 5$. Multiply both sides by 2: $x < 10$. Multiplying by 2 is safe because 2 is positive, so the sign does not flip. Subtracting 1 instead gives $x < 6$, and dividing by 2 gives $x < 2.5$.

4. 4.

   Which ordered pair is the solution of the system $y = 2x + 1$ and $y = -x + 7$?

   • A.

     $(5, 2)$

   • B.

     $(2, 5)$

   • C.

     $(2, 3)$

   • D.

     $(-2, -3)$

   Answer: B.

   Set the expressions for $y$ equal: $2x + 1 = -x + 7$, so $3x = 6$ and $x = 2$. Then $y = 2(2) + 1 = 5$, so the solution is $(2, 5)$. Check in the second equation: $-2 + 7 = 5$. The pair $(5, 2)$ reverses the coordinates.

5. 5.

   Which expression is equivalent to $(2x^2 + 3x - 1) - (x^2 - 4x + 5)$?

   • A.

     $x^2 - x + 4$

   • B.

     $x^2 - x - 6$

   • C.

     $x^2 + 7x - 6$

   • D.

     $x^2 + 7x + 4$

   Answer: C.

   Subtracting the second polynomial changes the sign of every term in it: $2x^2 + 3x - 1 - x^2 + 4x - 5$. Combine like terms: $x^2 + 7x - 6$. Changing only the sign of $x^2$ gives $x^2 - x + 4$, and forgetting to change the sign of the 5 gives $x^2 + 7x + 4$.

6. 6.

   What value of $x$ makes the equation $5x - 9 = 2x + 12$ true?

   • A.

     $7$

   • B.

     $1$

   • C.

     $3$

   • D.

     $21$

   Answer: A.

   Subtract $2x$ from both sides: $3x - 9 = 12$. Add 9: $3x = 21$. Divide by 3: $x = 7$. Stopping at $3x = 21$ gives 21, and subtracting 9 instead of adding it gives $x = 1$.

7. 7.

   Which expression is equivalent to $3(2x - 4) - 5x$?

   • A.

     $x - 4$

   • B.

     $x - 12$

   • C.

     $11x - 12$

   • D.

     $-x - 12$

   Answer: B.

   Distribute the 3 to both terms: $6x - 12$. Then combine like terms: $6x - 5x = x$, giving $x - 12$. Distributing only to the first term gives $x - 4$, and adding $5x$ instead of subtracting gives $11x - 12$.

8. 8.

   Which of the following is the factored form of $x^2 - 5x - 14$?

   • A.

     $(x - 7)(x + 2)$

   • B.

     $(x + 7)(x - 2)$

   • C.

     $(x - 7)(x - 2)$

   • D.

     $(x + 7)(x + 2)$

   Answer: A.

   Look for two numbers that multiply to $-14$ and add to $-5$: $-7$ and $2$. So $x^2 - 5x - 14 = (x - 7)(x + 2)$. The pair $(x + 7)(x - 2)$ gives $+5x$, and $(x - 7)(x - 2)$ gives $+14$.

9. 9.

   Which expression is equivalent to $(2x^3)^2 \cdot x$?

   • A.

     $4x^6$

   • B.

     $2x^7$

   • C.

     $4x^7$

   • D.

     $4x^{12}$

   Answer: C.

   Raising a product to a power raises each factor: $(2x^3)^2 = 4x^6$. Multiplying by $x$ adds 1 to the exponent: $4x^7$. Forgetting to square the 2 gives $2x^7$, and multiplying exponents in the last step gives $4x^{12}$.

10. 10.

    What are the solutions of the equation $x^2 = 6x - 8$?

    • A.

      $x = -2$ or $x = -4$

    • B.

      $x = 2$ or $x = -4$

    • C.

      $x = -2$ or $x = 4$

    • D.

      $x = 2$ or $x = 4$

    Answer: D.

    Move everything to one side: $x^2 - 6x + 8 = 0$. Factor: $(x - 2)(x - 4) = 0$, so $x = 2$ or $x = 4$. The signs are the most common slip: $(x + 2)(x + 4)$ would expand to $x^2 + 6x + 8$.