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Math Grade 6-8 Answer Key

Math: Expressions and Equations

Writing, simplifying, and solving algebraic statements

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Math: Expressions and Equations

Writing, simplifying, and solving algebraic statements

Math - Grade 6-8

Instructions: Read each problem carefully. Simplify expressions and solve equations. Show your work in the space provided.
  1. 1

    Write an algebraic expression for the phrase: 7 more than a number n.

    The words more than tell you to add.

    The algebraic expression is n + 7. The words 7 more than mean to add 7 to the number n.
  2. 2

    Write an algebraic expression for the phrase: 4 times the sum of x and 3.

    The algebraic expression is 4(x + 3). First add x and 3, then multiply the result by 4.
  3. 3

    Simplify: 5a + 3a.

    Like terms have the same variable part.

    The simplified expression is 8a. You add the coefficients because both terms have the same variable a.
  4. 4

    Simplify: 12y - 5y + 2.

    The simplified expression is 7y + 2. Combine the like terms 12y and -5y to get 7y, and keep the constant 2.
  5. 5

    Evaluate 3m + 4 when m = 6.

    Replace the variable with the given number.

    The value is 22. Substitute 6 for m to get 3(6) + 4 = 18 + 4 = 22.
  6. 6

    Evaluate 2x - 7 when x = 9.

    The value is 11. Substitute 9 for x to get 2(9) - 7 = 18 - 7 = 11.
  7. 7

    Solve the equation: x + 8 = 15.

    Use the opposite operation of addition.

    The solution is x = 7. Subtract 8 from both sides of the equation to isolate x.
  8. 8

    Solve the equation: n - 6 = 13.

    The solution is n = 19. Add 6 to both sides of the equation to isolate n.
  9. 9

    Solve the equation: 5p = 35.

    Undo multiplication by dividing.

    The solution is p = 7. Divide both sides of the equation by 5 to find the value of p.
  10. 10

    Solve the equation: k/4 = 9.

    The solution is k = 36. Multiply both sides of the equation by 4 to isolate k.
  11. 11

    Solve the equation: 2x + 3 = 17.

    Undo addition first, then undo multiplication.

    The solution is x = 7. Subtract 3 from both sides to get 2x = 14, then divide both sides by 2.
  12. 12

    Solve the equation: 3y - 5 = 16.

    The solution is y = 7. Add 5 to both sides to get 3y = 21, then divide both sides by 3.
  13. 13

    A school sells notebooks for n dollars each. Write an expression for the total cost of 6 notebooks.

    Total cost equals number of items times cost per item.

    The expression is 6n. Since each notebook costs n dollars, multiply n by 6 for 6 notebooks.
  14. 14

    A rectangle has length x and width 5. Write an expression for its perimeter.

    The expression for the perimeter is 2x + 10. A rectangle has two lengths and two widths, so the perimeter is 2x + 2(5).
  15. 15

    The sum of a number and 12 is 20. Write and solve an equation.

    The word sum means addition.

    One correct equation is x + 12 = 20, and the solution is x = 8. Subtract 12 from both sides to solve the equation.
LivePhysics.com Math - Grade 6-8 - Answer Key