Algebra questions with solutions for grade 8

Grade 8 algebra questions are presented with solutions. Questions include solving equations, simplifying expressions, and expressions with fractions.

  1. Simplify the following algebraic expressions.

    A) \(-2x + 5 + 10x - 9\)

    B) \(3(x + 7) + 2(-x + 4) + 5x\)

  2. Simplify the expressions.

    A) \(\dfrac{2x - 6}{2}\)

    B) \(\dfrac{-x - 2}{x + 2}\)

    C) \(\dfrac{5x - 5}{10}\)

  3. Solve for x the following equations.

    A) \(-x = 6\)

    B) \(2x - 8 = -x + 4\)

    C) \(2x + \dfrac{1}{2} = \dfrac{2}{3}\)

    D) \(\dfrac{x}{3} + 2 = 5\)

    E) \(\dfrac{-5}{x} = 2\)

  4. Evaluate for the given values of \(x\) and \( y \).

    A) \(x^2 - y^2\), for \(x = 4\) and \(y = 5\)

    B) \(|4x - 2y|\), for \(x = -2\) and \(y = 3\)

    C) \(3x^3 - 4y^4\), for \(x = -1\) and \(y = -2\)

  5. Solve the following inequalities.

    A) \(x + 6 < 0\)

    B) \(x + 1 > 5\)

    C) \(2(x - 2) < 12\)

  6. What is the reciprocal of each of the following numbers?

    A) \(-1\)

    B) \(0\)

    C) \(\dfrac{3}{4}\)

    D) \(2\dfrac{5}{7}\)

    E) \(0.02\)

  7. Evaluate the following expressions involving mixed numbers.

    A) \(3\dfrac{3}{4} + 6\dfrac{1}{7}\)

    B) \((1\dfrac{3}{5}) \times (3\dfrac{1}{3}) - 2\dfrac{1}{2}\)

    C) \((5\dfrac{2}{3}) \div (4\dfrac{1}{5})\)

    D) \((3\dfrac{4}{7} - 1\dfrac{1}{2}) \div (2\dfrac{3}{8} + 2\dfrac{1}{4})\)

  8. Evaluate the following exponential expressions.

    A) \(-4^2\)

    B) \((-2)^3\)

    C) \((-2)^4\)

    D) \(1000^0\)

    E) \(566^1\)

  9. Convert to fractions and write in simplest form.

    A) \(0.02\)

    B) \(12\%\)

    C) \(0.5\%\)

    D) \(1.12\)

  10. Convert to decimals.

    A) \(\dfrac{1}{5}\)

    B) \(120\%\)

    C) \(0.2\%\)

    D) \(4\dfrac{8}{5}\)

  11. Convert to percent.

    A) \(\dfrac{3}{10}\)

    B) \(1.4\)

    C) \(123.45\)

    D) \(2\dfrac{4}{5}\)

  12. Which of these numbers is divisible by 3?

    A) \(156312\)

    B) \(176314\)

  13. Which of these numbers is divisible by 4?

    A) \(3432\)

    B) \(1257\)

  14. Which of these numbers is divisible by 6?

    A) \(1233\)

    B) \(3432\)

  15. Which of these numbers is divisible by 9?

    A) \(2538\)

    B) \(1451\)

  16. Evaluate \(8x + 7\) given that \(x - 3 = 10\).

Solutions to the Above Questions

  1. A) \(-2x + 5 + 10x - 9\)

    \(= (10x - 2x) + (5 - 9)\)

    put like terms together

    \(= 8x - 4\)

    group

    B) \(3(x + 7) + 2(-x + 4) + 5x\)

    \(= 3x + 21 - 2x + 8 + 5x\)

    expand

    \(= (3x - 2x + 5x) + (21 + 8)\)

    put like terms together

    \(= 6x + 29\)

    group
  2. A) \(\dfrac{2x - 6}{2}\)

    \(= \dfrac{2(x - 3)}{2}\)

    factor 2 in numerator

    \(= x - 3\)

    divide numerator and denominator by 2 to simplify

    B) \(\dfrac{-x - 2}{x + 2}\)

    \(= \dfrac{-1(x + 2)}{x + 2}\)

    factor -1 in numerator

    \(= -1\)

    divide numerator and denominator by x + 2 to simplify

    C) \(\dfrac{5x - 5}{10}\)

    \(= \dfrac{5(x - 1)}{10}\)

    factor 5 in numerator

    \(= \dfrac{x - 1}{2}\)

    divide numerator and denominator by 5 to simplify
  3. A) \(-x = 6\)

    \(x = -6\)

    multiply both sides of the equation by -1

    B) \(2x - 8 = -x + 4\)

    \(2x - 8 + 8 = -x + 4 + 8\)

    add +8 to both sides of the equation

    \(2x = -x + 12\)

    group like terms

    \(2x + x = -x + 12 + x\)

    add +x to both sides

    \(3x = 12\)

    group like terms

    \(x = 4\)

    multiply both sides by 1/3

    C) \(2x + \dfrac{1}{2} = \dfrac{2}{3}\)

    \(2x + \dfrac{1}{2} - \dfrac{1}{2} = \dfrac{2}{3} - \dfrac{1}{2}\)

    subtract 1/2 from both sides

    \(2x = \dfrac{1}{6}\)

    group like terms

    \(x = \dfrac{1}{12}\)

    multiply both sides by 1/2

    D) \(\dfrac{x}{3} + 2 = 5\)

    \(\dfrac{x}{3} + 2 - 2 = 5 - 2\)

    subtract 2 from both sides

    \(\dfrac{x}{3} = 3\)

    group like terms

    \(x = 9\)

    multiply both sides by 3

    E) \(\dfrac{-5}{x} = 2\)

    \(-5 = 2x\)

    multiply both sides by x and simplify

    \(x = -\dfrac{5}{2}\)

    multiply both sides by 1/2
  4. A) \(x^2 - y^2\), for \(x = 4\) and \(y = 5\)

    \(4^2 - 5^2\)

    substitute x and y by the given values

    \(= 16 - 25 = -9\)

    evaluate

    B) \(|4x - 2y|\), for \(x = -2\) and \(y = 3\)

    \(|4(-2) - 2(3)|\)

    substitute x and y by the given values

    \(= |-8 - 6| = |-14| = 14\)

    evaluate

    C) \(3x^3 - 4y^4\), for \(x = -1\) and \(y = -2\)

    \(3(-1)^3 - 4(-2)^4\)

    substitute x and y by the given values

    \(= 3(-1) - 4(16) = -3 - 64 = -67\)

    evaluate
  5. A) \(x + 6 < 0\)

    \(x + 6 - 6 < 0 - 6\)

    subtract 6 from both sides

    \(x < -6\)

    group like terms

    B) \(x + 1 > 5\)

    \(x + 1 - 1 > 5 - 1\)

    subtract 1 from both sides

    \(x > 4\)

    group like terms

    C) \(2(x - 2) < 12\)

    \(x - 2 < 6\)

    multiply both sides by 1/2

    \(x - 2 + 2 < 6 + 2\)

    add 2 to both sides

    \(x < 8\)

    group like terms
  6. A) \(-1\)

    \((-1) \cdot a = 1\)

    definition: a is the reciprocal of -1

    \(a = \dfrac{1}{-1} = -1\)

    solve for a; -1 is the reciprocal of -1

    B) \(0\)

    \((0) \cdot b = 1\)

    definition: b is the reciprocal of 0

    \(b = \text{undefined}\)

    no value of b satisfies the above equation

    C) \(\dfrac{3}{4}\)

    \(\dfrac{3}{4} \cdot c = 1\)

    definition: c is the reciprocal of 3/4

    \(c = \dfrac{4}{3}\)

    solve for c; c = 4/3 is the reciprocal of 3/4

    D) \(2\dfrac{5}{7}\)

    \(2\dfrac{5}{7} \cdot d = 1\)

    definition: d is the reciprocal of 2 5/7

    \(\dfrac{19}{7} \cdot d = 1\)

    convert the mixed number 2 5/7 into a fraction

    \(d = \dfrac{7}{19}\)

    solve for d; d = 7/19 is the reciprocal of 2(5/7)

    E) \(0.02\)

    \(0.02 \cdot d = 1\)

    definition: d is the reciprocal of 0.02

    \(d = \dfrac{1}{0.02} = 50\)

    solve for d; d = 50 is the reciprocal of 0.02
  7. A) \(3\dfrac{3}{4} + 6\dfrac{1}{7}\)

    \(= (3 + 6) + (\dfrac{3}{4} + \dfrac{1}{7})\)

    put the whole parts together and the fractional parts together

    \(= 9 + (\dfrac{21}{28} + \dfrac{4}{28})\)

    add

    \(= 9\dfrac{25}{28}\)

    simplify
  8. A) \(-4^2\)

    \(= -(4 \times 4) = -16\)

    expand and calculate

    B) \((-2)^3\)

    \(= (-2) \times (-2) \times (-2) = -8\)

    expand and calculate

    C) \((-2)^4\)

    \(= (-2) \times (-2) \times (-2) \times (-2) = 16\)

    expand and calculate

    D) \(1000^0\)

    \(= 1\)

    definition: any nonzero number to the power zero gives 1

    E) \(566^1\)

    \(= 566\)

    any number to the power 1 is the number itself
  9. Evaluate \(8x + 7\) given that \(x - 3 = 10\).

    \(x - 3 = 10\)

    given equation

    \(x = 10 + 3 = 13\)

    solve the given equation

    \(8(13) + 7 = 104 + 7 = 111\)

    substitute x by 13 in the given expression and evaluate