Grade 8 Algebraic Equations Quiz 4 draws its questions at random from 33 questions across these topics:
A few of the question types, with full solutions, so you know what to expect.
Vocabulary. Which of these is an equation rather than an expression?
Answer: \(7x - 3 = 18\)
An equation contains an equals sign and makes a claim that can be solved.
The other three are expressions - you can only simplify them, not solve them.
Tip: If a question says "simplify" you have an expression. If it says "solve" you have an equation.
Vocabulary. In the equation \(5x + 8 = 28\), what is the left-hand side?
Answer: \(5x + 8\)
Everything before the equals sign is the left-hand side (LHS).
Everything after it is the right-hand side (RHS), which here is \(28\).
Vocabulary. In the equation \(5x + 8 = 28\), what is the coefficient of \(x\)?
Answer: \(5\)
The coefficient is the number multiplying the variable.
In \(5x\), the variable \(x\) is multiplied by \(5\).
Tip: \(8\) is the constant term - it has no variable attached.
Vocabulary. The value that makes an equation true is called the:
Answer: Solution (or root)
Solving an equation means finding the value that makes both sides equal.
That value is the solution, also called the root.
Vocabulary. Why must you do the same operation to both sides of an equation?
Answer: To keep the two sides equal, so the equation stays true
An equation is like a balance scale that is currently level.
Changing one side only tips the scale - the new equation is no longer true.
Tip: This one rule is behind every method for solving equations.