Grade 7

Linear Equations

The algebra of a single unknown, built from writing an expression up to equations with brackets, with fractions, and hidden inside word problems.

6 lessons

  1. 1How do you turn a sentence into an algebraic expression?Choose a letter to stand for the number you do not know, then translate the sentence operation by operation: more is addition, times is multiplication, less is subtraction. An expression describes a quantity and has no equals sign; an equation claims two quantities are equal, and that is what can be solved.30m
  2. 2How do you collect like terms and expand brackets?Like terms carry the same letter to the same power, and only those can be combined: three x plus two x is five x, but three x plus two stays as it is. The distributive law says to multiply whatever stands before the brackets by every term inside them, skipping none.35m
  3. 3How do you solve a first degree equation?An equation is a balance: as long as you do the same thing to both sides, the equality holds. Isolate the unknown using inverse operations — subtract what was added, divide by what multiplied — working in the reverse of the order of operations. Then substitute the solution back to check it.30m
  4. 4How do you solve an equation with the unknown on both sides?Gather the unknown on one side and the numbers on the other, then solve as usual. Moving a term across flips its sign, because moving is shorthand for subtracting that term from both sides. It is convenient to gather the unknown on whichever side has the larger coefficient, so it stays positive.30m
  5. 5How do you solve an equation with brackets and with fractions?Expand the brackets first, then clear the denominators by multiplying the whole equation by the common denominator. The multiplication has to reach every term on both sides, not only the fractions — that is the mistake which ruins most exercises in this topic. After those two steps a familiar equation is left.40m
  6. 6How do you turn a word problem into an equation?Decide what the unknown stands for and write it out in a full sentence, because everything else follows from that choice. Express the other quantities using the same unknown, translate the sentence that creates an equality into an equation, solve, and then return to the question — it often asks for something other than the unknown itself.40m