Grade 8 Algebraic Equations Quiz 6 draws its questions at random from 24 questions across these topics:
A few of the question types, with full solutions, so you know what to expect.
Expression or equation?. Which of these is an EQUATION?
Answer: \(3x + 5 = 14\)
An equation has an equal sign. An expression does not.
Tip: An expression you simplify. An equation you solve, because it makes a claim you can test.
Words to equations. Write an equation for: "A number increased by 9 is 23."
Answer: \(x + 9 = 23\)
"Increased by 9" means add 9, so \(x + 9\).
"Is" means equals.
Tip: The word "is" is where your equal sign goes. Without it you have only written an expression.
Words to equations. Solve: \(x + 9 = 23\).
Answer: \(x = 14\)
9 was added, so subtract 9 from both sides.
\(x = 23 - 9 = 14\)
Tip: Check it: \(14 + 9 = 23\). True.
The "less than" trap. Write an expression for: "5 less than a number."
Answer: \(x - 5\)
Try it with a real number. 5 less than 12 is 7.
That is \(12 - 5\), not \(5 - 12\).
Tip: "Less than" REVERSES the order you read it in. This is the commonest translation mistake in Grade 8.
Money problems. Five identical pens cost R45. What does one pen cost?
Answer: R9
Let \(x\) be the cost of one pen.
\(5x = 45\)
\(x = 45 \div 5 = 9\)