This course teaches you to solve linear equations in one variable, the most used tool in school algebra. It starts with what an equation is, what makes it linear and how to check a solution. You then learn the balance method and its shortcut, transposing, before moving on to equations with the variable on both sides, brackets, fractions and decimals, and equations that reduce to linear form by cross multiplication. The last two lessons turn word problems into equations: numbers, consecutive numbers, ratios, digits and fractions, then ages, coins and notes, shapes and journeys. Every lesson has worked examples and practice with answers.
Middle Years
Linear Equations in One Variable
What a linear equation in one variable is, how to solve it by balancing and transposing, how to handle brackets, fractions and decimals, and how to turn word problems into equations.
- 6 lessons
Overview
Lessons
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What a linear equation is
Expressions and equations, the LHS and RHS, what makes an equation linear in one variable, what a solution is, how to check one, and how to write an equation from words.
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Solving equations by balancing and transposing
The four balance rules, one-step and two-step equations, and transposing: moving a term across the equals sign changes its operation. Includes negative and fraction answers.
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Variables on both sides and brackets
Collect the variable on one side, open brackets with care when a minus sign stands in front, and spot the two special cases: an identity and an equation with no solution.
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Equations with fractions and decimals
Clear fractions by multiplying by the L.C.M. of the denominators, clear decimals with 10 or 100, and solve equations reducible to linear form by cross multiplication.
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Word problems on numbers
Five steps for any word problem, then two linked numbers, consecutive integers, even, odd and multiples, numbers in a ratio, two-digit numbers and fractions.
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Word problems on ages, money and shapes
Equations from problems on present and future ages, coins and notes, the perimeter of a rectangle, the angles of a triangle, and two-part journeys.