Simple Linear Equations (Including Word Problems)

What this chapter covers

• Equations and the words used with them
• The solution of an equation
• Solving an equation like a balance
• Solving equations with two operations
• The transposition method
• Turning words into equations
• Solving word problems
• Common errors to avoid

Key points

• An equation is a statement that two expressions are equal; it has a left-hand side, an equals sign and a right-hand side.
• A linear equation in one variable has a single variable, which appears only to the first power.
• The solution, or root, is the value of the variable that makes LHS equal to RHS; substituting it back checks it.
• An equation stays true if you add, subtract, multiply or divide both sides by the same number (never divide by zero).
• With two operations, undo them in reverse order: usually the added or subtracted number first, then the multiplier or divisor.
• Transposition moves a term across the equals sign and changes its operation to the inverse: + to -, - to +, × to ÷, ÷ to ×.
• Solutions can be negative numbers or fractions.
• For a word problem: name the unknown, form the equation, solve it, answer in words with units, and check against the story.

Questions answered