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Linear Equations

2.0 Algebra · 2.2 Linear Equations

Syllabus tag: Kenya CBC | Grade 7 Mathematics | Strand 2.0 Algebra | Sub-Strand 2.2 Linear Equations (6 lessons)

Lesson objectives

By the end of this topic, you will be able to:

  • Form linear equations in one unknown from different situations
  • Solve linear equations in one unknown
  • Apply linear equations to real-life situations
  • Reflect on the use of linear equations in real-life situations

Linear Equations

An equation says two things are equal. Solving it means finding the value of the letter that makes the statement true.

a) Equation or expression

An expression has no equals sign: 3x + 4.

An equation has one: 3x + 4 = 19.

An expression can only be simplified. An equation can be solved.

b) The balance idea

An equation is like a balance. Both sides weigh the same.

Whatever you do to one side, you must do to the other. Take 4 from one side, take 4 from the other. Divide one side by 3, divide the other by 3.

Do that and the balance stays level. Do it to one side only and the equation stops being true.

c) Solving

Solving step by step Solving step by step 3x + 4 = 19 the equation 3x = 15 subtract 4 from both sides x = 5 divide both sides by 3 check → 3(5) + 4 = 19 put it back in

Work towards getting the letter alone on one side.

Undo the additions and subtractions first, then the multiplications and divisions. That is the reverse of the usual order of operations, because you are undoing rather than doing.

Always check by putting your answer back into the original equation.

d) Letters on both sides

If the letter appears on both sides, collect it on one side first.

Take 5x − 3 = 2x + 9. Subtract 2x from both sides to get 3x − 3 = 9. Add 3 to both sides to get 3x = 12, so x = 4.

Move the letter to whichever side keeps it positive. It saves mistakes with signs.

e) Equations with brackets

Expand the brackets first, then solve as usual.

Take 2(x + 3) = 14. Expand to 2x + 6 = 14. Subtract 6 to get 2x = 8, so x = 4.

Multiply every term inside the bracket. Forgetting the second term is the usual slip.

f) Forming equations from words

From words to an equation From words to an equation let x be = the number of goats name the unknown in words = twice x, plus 5, is 23 the statement in algebra → 2x + 5 = 23 the equation solve → x = 9 nine goats

Name the unknown and say what it stands for.

Turn each piece of information into algebra, one phrase at a time.

Solve, then read the answer back in the words of the question. The answer is "nine goats", not just "9".

g) Where this is used

Working out a price from a total. Finding how many items were bought. Sharing an amount so that one person gets a stated amount more than another. Any question with one unknown and one fact about it.

Words to know

  • Linear equation — an equation in which the unknown appears only to the power of 1.
  • Isolate — to get the unknown alone on one side of an equation.
  • Balance principle — the rule that any operation applied to one side of an equation must also be applied to the other, to keep both sides equal.

:::checkpoint Check yourself

  1. Solve 4x − 7 = 21.
  2. Solve 6x + 2 = 4x + 14.
  3. Solve 3(x − 2) = 12.
  4. Twice a number added to 7 gives 25. Form an equation and solve it. :::

Bridge to practice

Try the exercises below — on forming and solving linear equations in one unknown.

Check yourselfPractise Linear Equations — 10 questions →Next in MathematicsFactors →