Basic Algebra Worksheet for 14‑Year‑Olds — Mathematics (Algebra) Practice

Free worksheet covering Mathematics, Algebra for age 14 students. Created with Learning Corner's AI-powered tools.

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Instructions

  1. Read the instructions for each section carefully before starting.
  2. In Sections 3, 4, and 5, your goal is to isolate the variable (x, k, n, or m) by using inverse operations.
  3. Show your work, especially for the equation solving tasks, in the provided space.
  4. Section 5 is an optional "Challenge" for advanced practice.

Section 1: Algebraic Translation (Vocabulary Check)

Translate the verbal phrases (Column A) into the correct algebraic expression (Column B). Write the corresponding letter in the 'Match' column.

Column A (Verbal Phrase) Column B (Algebraic Expression) Match (Write Letter)
Example: Five less than a number n D. 5 - n C
1. The quotient of a number x and 7 A. 4x + 12
2. A number y decreased by 15 B. x / 7
3. Four times a number x, increased by 12 C. n - 5
4. The product of 9 and a number z D. y - 15
5. 10 more than the product of 2 and k E. 9z
6. The difference between 18 and a number p F. 2k + 10
G. 18 - p

Section 2: Evaluating the Expression

If x = 4, y = -3, and z = 10, evaluate the following algebraic expressions. Show your substitution step.

  1. 2x + 5 (Substitution: 2(____) + 5) Value: _________________

  2. z - y (Substitution: ___________________________) Value: _________________

  3. xy - 8 (Substitution: ___________________________) Value: _________________

  4. x² + 2y Value: _________________

Section 3: Solving One-Step Equations

Solve for the variable (x or k). Identify the inverse operation you used to solve the equation.

Equation Inverse Operation Used Solution (Variable = ?)
Example: x + 7 = 15 Subtract 7 x = 8
1. x - 12 = 30
2. x + 9 = 21
3. 5k = 45
4. k / 4 = 11
5. -6x = 36

Section 4: Real-World Application (Two-Step Problems)

Solve these scenarios by following the three steps: Define the variable, write the equation, and solve the equation.

Scenario A: The Bookstore Budget

Ethan bought 3 new graphic novels and paid $5 for a mandatory reusable tote bag. His total bill was $44. How much did each graphic novel cost (n)?

  1. Define the variable (n): Cost of one graphic novel.

  2. Write the Equation:

  3. Solve the Equation (Show steps):

    n = _________________

Scenario B: The Fitness Class

A gym membership costs a $20 sign-up fee plus $15 per month (m). If Jane paid a total of $110, how many months has she been a member?

  1. Define the variable (m): Number of months Jane was a member.

  2. Write the Equation:

  3. Solve the Equation (Show steps):

    m = _________________

Section 5: The Algebra Challenge (Optional Extension)

Solve these slightly more complex equations that require multiple steps.

  1. (3x + 1) / 4 = 7

    x = _________________

  2. 4(y - 5) = 32

    y = _________________

Answer Key

Section 1: Algebraic Translation

Column A (Verbal Phrase) Column B (Algebraic Expression) Match (Write Letter)
Example: Five less than a number n D. 5 - n C
1. The quotient of a number x and 7 B. x / 7 B
2. A number y decreased by 15 D. y - 15 D
3. Four times a number x, increased by 12 A. 4x + 12 A
4. The product of 9 and a number z E. 9z E
5. 10 more than the product of 2 and k F. 2k + 10 F
6. The difference between 18 and a number p G. 18 - p G

Section 2: Evaluating the Expression

  1. 2x + 5 -> 2(4) + 5 = 8 + 5 = 13
  2. z - y -> 10 - (-3) = 10 + 3 = 13
  3. xy - 8 -> (4)(-3) - 8 = -12 - 8 = -20
  4. x² + 2y -> (4)² + 2(-3) = 16 - 6 = 10

Section 3: Solving One-Step Equations

Equation Inverse Operation Used Solution (Variable = ?)
1. x - 12 = 30 Add 12 x = 42
2. x + 9 = 21 Subtract 9 x = 12
3. 5k = 45 Divide by 5 k = 9
4. k / 4 = 11 Multiply by 4 k = 44
5. -6x = 36 Divide by -6 x = -6

Section 4: Real-World Application (Two-Step Problems)

Scenario A: The Bookstore Budget

  1. Write the Equation: 3n + 5 = 44
  2. Solve the Equation: 3n = 44 - 5 3n = 39 n = 13 n = 13 (Each novel cost $13)

Scenario B: The Fitness Class

  1. Write the Equation: 15m + 20 = 110
  2. Solve the Equation: 15m = 110 - 20 15m = 90 m = 6 m = 6 (Jane was a member for 6 months)

Section 5: The Algebra Challenge

  1. (3x + 1) / 4 = 7 3x + 1 = 28 3x = 27 x = 9

  2. 4(y - 5) = 32 y - 5 = 32 / 4 y - 5 = 8 y = 13 y = 13

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