Linear equations in one unknown

Skills and methods in this topic, easy to hard

1. 1Equations and the balanceDo the same to both sides and it stays level

   Method3x + 5 = 20, 3x = 15, x = 5

   Another way: Work backwards20 − 5 = 15, 15 ÷ 3 = 5

2. 2Unknowns on both sidesCross the equals sign, change the sign

   Method5x + 3 = 2x + 15, 5x − 2x = 15 − 3, x = 4

   Another way: Take from both sidesTake 2x from both: 3x + 3 = 15

3. 3Equations with bracketsOutside number times every term; a minus flips every sign

   Method3(x + 2) = 21, 3x + 6 = 21, x = 5

   Another way: Bracket as one thing3(x + 2) = 21, x + 2 = 7, x = 5

4. 4Fractions and decimals in equationsMultiply every term; a numerator is a bracket

   Methodx2 + x3 = 5, 3x + 2x = 30, x = 6

   Another way: Add the fractionsx2 + x3 = 5x6, 5x6 = 5, x = 6

5. 5From words to an equationOne quantity, written two ways, with an equals sign between

   Method3 less than twice x is 11: 2x − 3 = 11

   Another way: Choose the other as xx + (x + 3) = 15 or x + (x − 3) = 15

6. 6Word problems with equationsChoose, form, solve, then check it makes sense

   Method5x + 2(10 − x) = 35, 3x + 20 = 35, x = 5

   Another way: Suppose them all alikeAll $2: $20; (35 − 20) ÷ 3 = 5

Worked examples

From different skills in this topic. Have a go first, then open each one for the answer and the working.

1. Example 1Equations and the balance →

   3x + 12 = 30: take 12 from both sides, 3x = ; divide both by 3, x = .

   Fill in each blank

   ▶Show the answer and working

   Answer: 18, 6

   30 − 12 = 18, 18 ÷ 3 = 6. Check with x = 6: 3x + 12 = 18 + 12 = 30.

2. Example 2Fractions and decimals in equations →

   To clear the denominators of x10 + x8 = 7, what is the handiest number to multiply both sides by?

   • A. 40
   • B. 80
   • C. 18
   • D. 10

   Choose the right answer

   ▶Show the answer and working

   Answer: A. 40

   The L.C.M. of 10 and 8 is 40; times 40 clears both denominators.

3. Example 3Word problems with equations →

   Ka-lok has 49 marbles, May has 35. How many must Ka-lok give May to match?

   ▶Show the answer and working

   Answer: 7 marbles

   49 − x = 35 + x, 2x = 14, x = 7. Each one given closes the gap by 2.