Algebra 2: Solving Equations

Algebra 2:
Solving Equations

Speaking Algebra - Match up

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Function Machines

Going forwards = follow the instructions

Function machines are nice ways to do algebra, they tell us what to do in which order. We need to be careful about the different words they use.
Input = what we put in
Output = what we get out
"In terms of x" = your answer will be an expression not a number

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Multiple Choice

Give the output y in terms of x

• $$y=\frac{x}{2}+3$$

• $$x=\frac{y}{2}+3$$

• $$x=\frac{y+3}{2}$$

• $$y=\frac{x+3}{2}$$

Function Machines

Going backwards = backwards and opposite

Sometimes they are going to ask us to work out what went in (the input) if we know what the answer is (the output).
This can either be numbers OR expressions, depending on the function machine. Read the question carefully and double triple check you're going the right way!

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Multiple Choice

Work out the input when the output is -4

• -10

• 10

• -14

• 14

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Solving Equations

Work backwards and opposite to find x

When we're solving equations, we're basically trying to work backwards from the expression to work out what the missing number could have been to give us the answer on the other side. We need to undo all the things, so go backwards and inverse each step to find what we started with....

Match

Match each operation with its opposite (inverse)

• add

• subtract

• multiply

• divide

• square

subtract

add

divide

multiply

square root

• subtract

• add

• divide

• multiply

• square root

Multiple Choice

Find x when

x + 3 = 9

• 6
• 5
• 3
• 12

Multiple Choice

Find x when

x - 4 = 9

• 36

• 13

• 5

• 7

Multiple Choice

Find x when

20x = 800

• 4

• 40
• 780

• 400

Multiple Choice

Find x when

x ÷ 5 = 10

• 2

• 50

• 5

• 15

Multiple Choice

Find x when

$$\sqrt[]{x}=9$$

• x = 0.9

• x = 4.5

• x = 3

• x = 81

This is what my expression is REALLY telling me, so these are the things that need undoing and in reverse order.
19 - 7 = 12
12 ÷ 2 = 6 (so x = 6)

x → x2 → +7 → 19

This is called a 2-step equation because two things are being done to x, and two things need undoing to solve it.

2x + 7 = 19

Lovely. Now, two step equations

x ← ÷2 ← -7 ← 19

19 - 7 = 12
12 ÷ 2 = 6
x = 6

x → x2 → +7 → 19

2x + 7 = 19
2x = 12 (-7)
x = 6 (÷2)

2x + 7 = 19

We aren't layout snobs here.

​is just as
valid as

x ← ÷4 ← +6 ← 42

42 + 6 = 48
48 ÷ 4 = 12
x = 12

x → x4 → -6 → 42

4x - 6 = 42
4x = 48 (+6)
x = 12 (÷4)

4x - 6 = 42

Let's go again

​is just as
valid as

Multiple Choice

What step is FIRST to solve the equation

5x + 6 = 36?

• take away 6 from 36

• divide 36 by 5

• add 6 to 36

• multiply 36 by 5

Multiple Choice

What step is FIRST to solve the equation $$\frac{x}{4}\ -1=\ 9$$

• multiply 9 by 4

• divide 9 by 4

• add 1 to 9

• subtract 1 from 9

Multiple Choice

What step is FIRST when solving $$\frac{x+3}{9}=11$$

• divide 11 by 9

• multiply 11 by 9

• take away 3 from 11

• add 3 to 11

Multiple Choice

What step is FIRST when solving this equation?

$$2x^2\ =\ 32$$

• multiply 32 by 2

• divide 32 by 2

• square 32

• square root 32

1) 4a + 7 = 39

2) 7b – 8 = 55

3) 12c + 11 = 95

4) 9d – 6 = -33

5) 6e – 5 = 10

6) f² + 13 = 157

7) 89 = 15g + 9

8) 247 = 13 – 9h

Solving with brackets

4(2x - 11) = 36

Expand out first!
2x + 14 = 18
2x = 4
x = 2
x → x2 → +14 → 18
x ← ÷2 ← -14 ← 18
18 - 14 = 4
4 ÷ 2 = 2

2(x + 7) = 18

Draw

Solve

2(x + 1) = 22

Draw

Solve either the top or bottom equation:

Normal:

5(2x -4) = 50

Hard:

$$\frac{2}{5}\left(25x\ -\ 75\right)=-55$$

Solving equations with x on both sides

5y - 4 = 10y + 6

Step one: take away the smallest number of x's from BOTH SIDES
4x - 5 = x + 1 (now -x)
3x - 5 = 1 (now solve as you would normally)
(add 5, divide by 3, x = 2)

4x - 5 = x + 1

Reorder

Give the correct order of steps for solving:

3x + 2 = x +8

• subtract 1x from both sides

• take away 2 from 8

• divide by 2

• give the answer as x =

1

2

3

4

• 1
• 2
• 3
• 4

Reorder

Give the correct order of steps for solving:

2x + 1 = 7x - 4

• subtract 2x from both sides

• take 1 away from -4

• divide by 5

• give the answer as x =

1

2

3

4

• 1
• 2
• 3
• 4

Draw

Solve either the top or the bottom question:

Normal:

4x + 2 = 2x + 8

Hard:

4(x + 3) = 2(4x + 5)

Sorry.
Exam questions now!

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