solving equations foundation tier gcse. starter activity – evaluate when…... put the cards in...

Solving EquationsSolving Equations

Foundation Tier GCSEFoundation Tier GCSE

Starter Activity – Evaluate when…...Starter Activity – Evaluate when…...

Put the cards in order of smallest on the Put the cards in order of smallest on the left to largest on the right….when….left to largest on the right….when….

x = 10x = 10 x = 1x = 1 x = 3x = 3 x = -5 ( hard!!)x = -5 ( hard!!)

Aims for today’s lessonAims for today’s lesson

To understand what an equation is….To understand what an equation is…. To be able to make an equation…..To be able to make an equation….. To know what solving an equation To know what solving an equation

means, and be able to solve simple means, and be able to solve simple equationsequations

What What isis an Equation? an Equation? An equation looks a bit like the algebra we An equation looks a bit like the algebra we

were doing in earlier lessons……were doing in earlier lessons…… The key difference is suggested by the word The key difference is suggested by the word

itself……itself……

EQUALSEQUALS An equation always has an equals sign An equation always has an equals sign

somewhere (usually in the middle of the somewhere (usually in the middle of the problem).problem).

TIONS

How to make an Equation…How to make an Equation…

OK – think of a number…….OK – think of a number……. Double your number…..Double your number….. Subtract (take off) 3….Subtract (take off) 3…. You get the answer 9. What was the You get the answer 9. What was the

original number you thought of?original number you thought of?

How to make an Equation…How to make an Equation… OK – think of a number……. Call it xOK – think of a number……. Call it x Double your number………..that’s 2xDouble your number………..that’s 2x Subtract (take off) 3……….so 2x - 3Subtract (take off) 3……….so 2x - 3 You get the answer 9…..so 2x – 3 = 9You get the answer 9…..so 2x – 3 = 9 What was the original number you thought What was the original number you thought

of? of? Reverse the steps….start with the 9 …. Now Reverse the steps….start with the 9 …. Now

addadd 3….that’s 12….. 3….that’s 12…..dividedivide by 2….so my by 2….so my original number, original number, x = 6. x = 6. I now know what x is I now know what x is – which means I’ve solved my equation!!– which means I’ve solved my equation!!

How to make an Equation…How to make an Equation…

OK – think of a number…………xOK – think of a number…………x multiply your number by 5…….that’s 5xmultiply your number by 5…….that’s 5x add 2……………now that gives 5x + 2add 2……………now that gives 5x + 2 You get the answer 22…..so that’s 5x+2=22You get the answer 22…..so that’s 5x+2=22 Now to solve it…..start with the 22 Now to solve it…..start with the 22

… ..subtract the 2….that’s 20….divide by 5 … ..subtract the 2….that’s 20….divide by 5 … ..so … ..so x=4x=4

Solving Equations….Solving Equations….Example:Example: SolveSolve 3x + 4 = 253x + 4 = 25Method: Method: write the equation down:write the equation down:

3x + 4 = 253x + 4 = 25Subtract 4Subtract 4 from the equation….. from the equation…..

3x + 4 3x + 4 – 4– 4 = 25 = 25 – 4– 4 3x = 213x = 21

DivideDivide the equation by 3……. the equation by 3…….

x = 7x = 7 (Check!!)(Check!!)

Notice how an equation is like a balance – what you do to one side of the equals, you must also do on the other side…..

Now for theNow for the HUMAN HUMAN EQUATION!!EQUATION!!

Solve 4x + 6 = 20Solve 4x + 6 = 20

Solving Equations….2Solving Equations….2Example:Example: SolveSolve 77x - 5 = 30x - 5 = 30Method: Method: write the equation down:write the equation down:

7x - 5 = 307x - 5 = 30Add 5Add 5 to both parts of the equation…. to both parts of the equation….

7x - 5 7x - 5 + 5+ 5 = 30 = 30 + 5+ 5 7x = 357x = 35



Again – the equation is a balancing act….

Solving Equations….3Solving Equations….3Example:Example: SolveSolve 88x + 1 = 13x + 1 = 13Method: Method: write the equation down:write the equation down:

8x + 1 = 138x + 1 = 13Subtract 1Subtract 1 from both parts of the equation…. from both parts of the equation….

8x + 1 8x + 1 - 1- 1 = 13 = 13 - 1- 1 8x = 128x = 12


x = 1.5x = 1.5 (Check!!)(Check!!)

Here we do the same thing to both sides – but try to isolate the x term…

Equations on the web…..Equations on the web…..

Use 11-14, Equations, level 2Use 11-14, Equations, level 2

Review today’s lessonReview today’s lesson

To understand what an equation is….To understand what an equation is…. To be able to make an equation…..To be able to make an equation….. To know what solving an equation To know what solving an equation

means, and be able to solve simple means, and be able to solve simple equationsequations

Try this algebra pyramidTry this algebra pyramid

What is x to make this work?

24

2x

5

8


1.1. To know what solving an equation To know what solving an equation means, and be able to solve simple means, and be able to solve simple equations with only one equations with only one xx term term

2.2. To understand how to solve To understand how to solve equations with an equations with an xx term on each term on each side (grade C +)side (grade C +)

Solving Equations….Solving Equations….Example:Example: SolveSolve 22x + 14 = 25x + 14 = 25Method: Method: write the equation down:write the equation down:

2x + 14 = 252x + 14 = 25Subtract 14Subtract 14 from the equation….. from the equation…..

2x + 14 2x + 14 – 14– 14 = 25 = 25 – 14– 14 2x = 112x = 11


x = 5.5x = 5.5 (Check!!)(Check!!)

Notice how an equation is like a balance – what you do to one side of the equals, you must also do on the other side…..

Try these quickly…..Try these quickly…..Solve:Solve:

1.1. 3x + 6 = 153x + 6 = 15

2.2. 4x – 3 = 134x – 3 = 13

3.3. 5x + 2 = 275x + 2 = 27

4.4. 23 + 3x = 4423 + 3x = 44

5.5. 50 = 26 + 8x50 = 26 + 8x

Solving Equations with TWO Solving Equations with TWO xx terms terms

Example:Example: SolveSolve 3x + 4 = 2x + 93x + 4 = 2x + 9Method: Method: write the equation: 3x + 4 = 2x + 9write the equation: 3x + 4 = 2x + 9

Subtract 4Subtract 4 from the equation….. from the equation…..

3x + 4 3x + 4 – 4– 4 = 2x + 9 = 2x + 9 – 4– 4

3x = 2x + 53x = 2x + 5Now Now subtract 2xsubtract 2x from the equation ……. from the equation …….

3x 3x – 2x– 2x = 2x = 2x – 2x– 2x + 5 + 5



Example:Example: SolveSolve 5x - 6 = 3x + 85x - 6 = 3x + 8Method: Method: write the equation: 5x - 6 = 3x + 8write the equation: 5x - 6 = 3x + 8

Add 6 Add 6 to both sides of the equation….. to both sides of the equation…..

5x - 6 5x - 6 + 6+ 6 = 3x + 8 = 3x + 8 + 6+ 6

5x = 3x + 145x = 3x + 14Now Now subtract 3xsubtract 3x from both sides ……. from both sides …….

5x 5x – 3x– 3x = 3x = 3x – 3x– 3x + 14 + 14

Now Now 2x2x = 14 so = 14 so x = 7x = 7


Example:Example: SolveSolve x - 6 = 5x + 10x - 6 = 5x + 10Method: Method: SwapSwap the equation: 5x + 10 = x – 6 the equation: 5x + 10 = x – 6

Subtract 10 Subtract 10 from both sides of the equation…..from both sides of the equation…..

5x + 10 5x + 10 – 10 – 10 = x – 6 = x – 6 – 10 – 10

5x = x – 16 5x = x – 16 Now Now subtract xsubtract x from both sides ……. from both sides …….

5x 5x – x– x = x = x – x– x – 16 – 16

Now Now 4x = - 16 so 4x = - 16 so x = - 4x = - 4

Equations on the web…..Equations on the web…..

Use 11-14, Equations, level 4Use 11-14, Equations, level 4

These were the aims for today’s These were the aims for today’s lesson:lesson:

1.1. To know what solving an equation To know what solving an equation means, and be able to solve simple means, and be able to solve simple equations with only one equations with only one xx term term

2.2. To understand how to solve equations To understand how to solve equations with an with an xx term on each side (grade C +) term on each side (grade C +)

Now check your learning by having a go at Now check your learning by having a go at this question from a GCSE paper:this question from a GCSE paper:

Solve the equation x – 4 = 3(x + 1).

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......................................................................................

......................................................................................

......................................................................................

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Answer x = ................................................... (3 marks)


1.1. To understand how to solve To understand how to solve equations involving a divide and an equations involving a divide and an xx term (grade C ) term (grade C )

2.2. To know how to deal with brackets To know how to deal with brackets in the equation (grade C)in the equation (grade C)

Dealing with fractions…..Dealing with fractions…..

SolveSolve: : xx = 10 = 10 33

Now begin by looking carefully at what the equation is Now begin by looking carefully at what the equation is actuallyactually saying: saying:

“ “ x divided by 3 equals 10”x divided by 3 equals 10” or…. or….“ “ what number, divided by 3, is 10?”what number, divided by 3, is 10?”

The answer is obviously x = 30 – so it seems all you The answer is obviously x = 30 – so it seems all you need to do is let the 10 be multiplied by the 3…..In need to do is let the 10 be multiplied by the 3…..In fact, this must be right, because the opposite of divide fact, this must be right, because the opposite of divide by 3 by 3 isis multiply by 3….. multiply by 3…..

x = 30x = 30

Dealing with fractions 2Dealing with fractions 2

SolveSolve: : xx = 4 = 4 55

Again, what the equation is Again, what the equation is actuallyactually saying is: saying is:“ “ x divided by 5 equals 4”x divided by 5 equals 4” or…. or….“ “ what number, divided by 5, is 4?”what number, divided by 5, is 4?”

The answer is obviously x = 20 – so again all you The answer is obviously x = 20 – so again all you need to do is let the 4 be multiplied by the 5…..this need to do is let the 4 be multiplied by the 5…..this must be right, because the opposite of divide by 5 must be right, because the opposite of divide by 5 isis multiply by 5…..multiply by 5…..

x = 20x = 20

Dealing with fractions 3Dealing with fractions 3

SolveSolve: : xx + 6 = 10 + 6 = 10 22

First, First, take 6take 6 from both sides…..gives you…. from both sides…..gives you….xx = 4 = 422

Now Now multiply both sides by 2multiply both sides by 2…..giving:…..giving:x = 8x = 8

Dealing with fractions 4Dealing with fractions 4SolveSolve: : 22xx - 4 = 6 - 4 = 6

77

First, First, add 4add 4 to both sides…..gives you…. to both sides…..gives you….

2x 2x = 10 = 10

77

Now Now multiply both sides by 7multiply both sides by 7…..giving:…..giving:

22x = 70x = 70

Finally divide both sides by 2, giving….Finally divide both sides by 2, giving….

x = 35x = 35

These were the aims for today’s These were the aims for today’s lesson:lesson:

1.1. To understand how to solve equations To understand how to solve equations involving a divide and an involving a divide and an xx term (grade term (grade C +)C +)

2.2. To know how to deal with brackets in To know how to deal with brackets in the equation (grade C+)the equation (grade C+)

Now check your learning by having a go at Now check your learning by having a go at this question from a GCSE paper:this question from a GCSE paper:

Solve these equations.

(a) 3p 5 = 7

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Answer p = .................................................................................................................

(b) 3

q = 4

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Answer q = .................................................................................................................

(c) 2(x + 3) = 11

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Answer x = .................................................................................................................

(d) 4y+7= 2 y

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Answer y= ............................................................................................................ .......

solving equations foundation tier gcse. starter activity – evaluate when…... put the cards in...

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