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Grade 8 Algebraic Equations Quiz 1

Equation Language and Solving by Inspection

What this quiz covers

grade8_equations_quiz1 draws its questions at random from a bank of 10 questions, with full worked solutions for every one.

Worked examples

A few of the question types, with full solutions, so you know what to expect.

Which of the following is an equation, not just an expression?

  1. \(5p+2\)
  2. \(5p+2=17\)
  3. \(3(4)+1\)
  4. \(7x\)

Answer: \(5p+2=17\)

\(\text{An equation contains an equals sign relating two expressions.}\)

\(\text{Only } 5p+2=17 \text{ has an equals sign.}\)

In the equation \(4a-9=15\), what is the constant term (with its sign)?

  1. 4
  2. \(a\)
  3. \(-9\)
  4. 15

Answer: \(-9\)

\(\text{A constant is a number without a variable attached.}\)

\(\text{The term } -9 \text{ has no variable, so it is the constant.}\)

Solve by inspection: \(x+7=15\)

  1. \(x=8\)
  2. \(x=22\)
  3. \(x=7\)
  4. \(x=105\)

Answer: \(x=8\)

\(\text{Ask: what number plus 7 equals 15?}\)

\(x=8\)

\(\text{Check: } 8+7=15\)

Solve by inspection: \(21-a=9\)

  1. \(a=30\)
  2. \(a=12\)
  3. \(a=-12\)
  4. \(a=9\)

Answer: \(a=12\)

\(\text{Ask: what must be subtracted from 21 to give 9?}\)

\(a=12\)

\(\text{Check: } 21-12=9\)

Solve by inspection: \(4m=28\)

  1. \(m=6\)
  2. \(m=32\)
  3. \(m=7\)
  4. \(m=112\)

Answer: \(m=7\)

\(\text{Ask: what number multiplied by 4 equals 28?}\)

\(m=7\)

\(\text{Check: } 4(7)=28\)