Solving Linear Equations Grades D to B

Starter – I think of a number Simple equations Trial and improvement Single bracket Hyperlinks! Letters on both sides Containing x² Fractional parts

Some “I think of a number…” questions to warm you up. For starters… Some “I think of a number…” questions to warm you up.

Explain how you worked that out. I think of a number… I think of a number and multiply it by 4. My answer is 20. What was my number? Answer: 5 Explain how you worked that out. I think of a number and subtract 7 from it. My answer is 11. What was my number? Answer: 18

Explain how you worked that out. I think of a number… I think of a number, multiply it by 2, then add 3. My answer is 17. What was my number? Answer: 7 Explain how you worked that out. I think of a number, subtract 2, then divide by 3. My answer is 6. What was my number? Answer: 20

What have you just been doing? Answer: Solving equations

Solving equations with a letter on one side Lesson Objective: How do I solve a two-step equation? Grade D

SUCCESS CRITERIA: WHERE ARE WE NOW? Level Learning outcomes: R A G D2 I can solve equations with a letter on one side.   C3 I can solve equations containing a bracket. C1 I can solve equations with letters on both sides.

The solution is the value of one letter. You must remember: 3𝑥 means 3×𝑥. 𝑥 3 means 𝑥÷3. The solution is the value of one letter. Show all your working out to prove to whoever is marking it that you know what you are doing. The answer on its own often isn’t enough.

Some examples Example 1 Example 2 Solve 4𝑥=28. “4 times a number is 28” The letter is multiplied by 4, so we must divide 28 by 4 So 𝑥=28÷4 𝑥=7 Solve 𝑥 6 =3 “A number divided by 6 is 3” The letter is divided by 6, so we must multiply 3 by 6. So 𝑥=3×6 𝑥=18

Have a go at these: 𝑥+7=18 𝑔−5=9 15−ℎ=9 17=𝑏+11 4𝑦=12 7𝑎=35 𝑛 8 =5 𝑥 12 =4 Answers: 𝑥=11 𝑔=14 ℎ=6 𝑏=6 𝑦=3 𝑎=5 𝑛=40 𝑥=48

The part under my hand must equal 12. A little tougher… Solve 2𝑥+3=15. “2 times a number, plus 3 is 15” Cover the lettered bit: 2𝑥+3=15. The part under my hand must equal 12. 2𝑥=12 𝑥=6

The part under my hand must equal 35. And another: Solve 5𝑥−4=31. “5 times a number, take away 4 is 31” Cover the lettered bit: 5𝑥−4=31. The part under my hand must equal 35. 5𝑥=35 𝑥=7

Try These: 3𝑥+2=23 7𝑦−3=18 9𝑐−4=41 20−2𝑥=12 25−8𝑦=1 Answers: 𝑥=7 𝑦=3 c=5 𝑥=4

SUCCESS CRITERIA: WHERE ARE WE NOW? Level Learning outcomes: R A G D2 I can solve equations with a letter on one side.   C3 I can solve equations containing a bracket. C1 I can solve equations with letters on both sides.

Solving equations with a bracket Lesson Objective: How do I solve a two-step equation that contains a bracket? Grade C

SUCCESS CRITERIA: WHERE ARE WE NOW? Level Learning outcomes: R A G D2 I can solve equations with a letter on one side.   C3 I can solve equations containing a bracket. C1 I can solve equations with letters on both sides.

What to do with brackets Solve 5(𝑥−4)=35. “A number take away 4, then times 5 is 35” Cover the lettered bit: 5(𝑥−4)=35. The part under my hand must equal 7. 𝑥−4=7 𝑥=11

The part under my hand must equal 11. And another: Solve 3(𝑥+5)=33. “A number add 5, then times 3 is 33” Cover the lettered bit: 3(𝑥−5)=33. The part under my hand must equal 11. 𝑥+5=11 𝑥=6

Try These: 3(𝑥+2)=15 4(𝑦−3)=16 8(𝑐+5)=48 5(7−𝑥)=15 2(5−𝑦)=14 Answers: 𝑥=3 𝑦=7 c=1 𝑥=4 𝑦=−2

The part under my hand must equal 11. A little tougher: Solve 3(2𝑥+5)=33. “Two times a number add 5, then times 3 is 33” Cover the lettered bit: 3(𝑥−5)=33. The part under my hand must equal 11. 2𝑥+5=11 2𝑥=6 𝑥=3

The part under my hand must equal 10. And another: Solve 4(3𝑥−2)=40. “Two times a number add 5, then times 3 is 33” Cover the lettered bit: 4(3𝑥−2)=40. The part under my hand must equal 10. 3𝑥−2=10 3𝑥=12 𝑥=4

Try These: 3(4𝑥+1)=15 4(2𝑦−3)=20 5(3𝑐+4)=50 10(7−2𝑥)=30 3(5−2𝑦)=27 Answers: 𝑥=1 𝑦=4 c=2 𝑥=2 𝑦=−2

SUCCESS CRITERIA: WHERE ARE WE NOW? Level Learning outcomes: R A G D2 I can solve equations with a letter on one side.   C3 I can solve equations containing a bracket. C1 I can solve equations with letters on both sides.

Solving equations with letters on both sides. Lesson Objective: How do I solve an equation where letters appear on both sides of the equals? Grade C

SUCCESS CRITERIA: WHERE ARE WE NOW? Level Learning outcomes: R A G D2 I can solve equations with a letter on one side.   C3 I can solve equations containing a bracket. C1 I can solve equations with letters on both sides.

The letter appears on both sides! In order to solve an equation where the letter appears on both sides of the equals, you must get the lettered parts on one side and the numbers on the other. We do this by “balancing” the equation.

There was one more 𝑥 on the left hand side Example 1 Solve 3𝑥 −2=2𝑥+7. What the difference between the number of 𝑥’s on both sides? 𝑥−2=7 There was one more 𝑥 on the left hand side Answer: 𝑥=9

There were two more 𝑥’s on the left hand side Example 2 Solve 7𝑥−2=5𝑥+8. What the difference between the number of 𝑥’s on both sides? 2𝑥−2=8 There were two more 𝑥’s on the left hand side 2𝑥−2=8 2𝑥=10 Answer: 𝑥=5

There were three more 𝑥’s on the left hand side Example 3 Solve 2𝑥+11=5𝑥−1. What the difference between the number of 𝑥’s on both sides? 11=3𝑥−1 There were three more 𝑥’s on the left hand side 11=3𝑥−1 12=3𝑥 Answer: 𝑥=4

Try These: 3𝑥−4=𝑥+6 4𝑥+3=5𝑥+1 5𝑦−11=𝑦+5 4𝑎+3=2𝑎−3 5(𝑥−2)=2(𝑥+1) Answers: 𝑥=5 𝑥=2 y=4 𝑎=−3 𝑥=4

SUCCESS CRITERIA: WHERE ARE WE NOW? Level Learning outcomes: R A G D2 I can solve equations with a letter on one side.   C3 I can solve equations containing a bracket. C1 I can solve equations with letters on both sides.