Solving Equations

Question 1

Solve 3x-4=11

Answer 1

3x-4=11
(+4 to both sides)
3x=15
(Divide by 3)
X=5

Question 2

Solve 3x/4 -1 =10

Answer 2

3x/4 -1 = 10
(+1)
3x/4=11
(X4)
3x=44
(Divide by 3)
X=44/3

Question 3

Solve 5-2x=10

Answer 3

5-2x=10
(-5)
-2x=5
(Divide by 2)
X=-5/2
X=-2.5

Question 4

Solve 3(2x-5)=10

Answer 4

6x=-15=10
/+15
6x=25
/divided by 6
X=25/6
=4 1/6

Question 5

Solve 12=3(4x+1)+2

Answer 5

12=3(4x+1)+2
12=12x+3+2
12=12x+5
/-5
7=12x
/divide by 12
7/12=x

Question 6

Solve 5-2(3x-4)=10

Answer 6

5-6x+8=10
13-6x=10
/-13
-6x=-3
/divide by -6
X=-3/-6
(Negative divided by negative = positive)
X=3/6=1/2

Question 7

Solve 4x -3 = 2x+1

Answer 7

/-2x
2x-3=1
/+3
2x=4
(Divide by 2
X=2

Question 8

Solve 6-3x=8x+2

Answer 8

/+3x
6=11x+2
/-2
4=11x
/divide by 11
4/11=x

Question 9

Solve 3x -2 = 10- 8x

Answer 9

/+8x
11x-2=10
/+2
11x=12
/divide by 11
X=12/11

Question 10

Solve 3(2x-1)=2(4-5x)

Answer 10

6x-3=8-10x
/+10x
16x=11
/+3
16x=11
/divided by 16x
X = 11/16

Question 11

Solve 2(5y-1)=3(2y+1)-4

Answer 11

10y-2=6y+3-4
10y-2=6y-1
/-6y
4y-2=-1
/+2
4y=1
Y=1/4

Question 12

Kevin thinks of a number then adds 7. His answer is 19. Work out the number Kevin is thinking of.

Answer 12

x +7=19
/-7
X=12

Question 13

a) write an expression, in terms of x, for the sum of the angels of this triangle

X
\ \
  \.      \
   \\_\_\_\_\_2x_\
  ^2x+90*

Answer 13

An expression has no equal sign
a) x +2x +90 + 2x
=5x + 90

Three angles on a triangle add up to 180*
b) 5x+90=180
/-90
5x=90
/divided by 5
X=18

Largest angle =2x+90
=2x18+90
=126*

Question 14

Solve 16-x/4 =1-x

Answer 14

/x4
16-x = 4-4x
/+4x
16+3x=4
/-16
3x=-12
/divided by 3
X=-4

Question 15

Solve 2x-1/2 - x-5/3 =5/4

Answer 15

Make a common denominator
6(2x-1)/12   - 4(x-5)/12     =15/12
/x12
6(2x-1) -4(x-5)=15
Expand the brackets
12x-6-4x+20=15
8x+14=15
/-14
8x=1
/divided by 8
X=1/8

Question 16

How do we work out the square root of a negative number?

Answer 16

We don’t, it’s impossible

Question 17

What does it mean for something to be quadratic?

Answer 17

It has an x^2

Question 18

Solve x^2+5x+6=0

Answer 18

Factorise to help solve the equation, insure it equals 0 first
(X+2)(x+3)=0
X=-3 or -2
One of these (either the +2 or +3) must add with x to make 0

Question 19

What’s special about a solving a quadratic answer?

Answer 19

It has two answers

Question 20

Solve x^2-7x+12=0

Answer 20

(X-3)(x-4)=0

X=3 or x=4

Question 21

Solve x^2-8x+17=2

Answer 21

/-2
X^2-8x+15=0
(X-5)(x-3)=0
X=5 or x=3

Question 22

What is the rule for dividing by an unknown?

Answer 22

Don’t

Question 23

Solve x^2 = 4x+12

Answer 23

You need to make it equal to 0
/-4x
X^2-4x=12
/-12
X^2-4x-12=0
(X-6)(x+2)=0

Question 24

Solve: 2x^2 + 11x + 12 = 0

Answer 24

(Smiley face method)
(2x+3)(x+4)=0
3xX=3x
4x2X=8x

X=-4

2x+3=0
/-3
2x-3
/divided by 2
X=-3/2

X= -4 or -3/2

Question 25

Solve 3x+2y=13

5x+2y=19

Answer 25

5x+2y=19
Take away    3x+2y=13
               =     2x =6
/divide by 2
X=3

Sub x=3 into a]A or B

A:3x+2y =13
3x3 +2y =13
9+2y=13
2y=4
Y=2

Question 26

Solve 4x +3y=8

6x+3y=9

Answer 26

6x+3y=9
Take away 4x+3y=8
= 2x=1
/divide by 2
X=1/2

Sub x=1/2 into A or B
4x+3y=8
4x1/2+3y=8
2+3y=8
3y=6
Y=2

Question 27

Solve x^2=4x+12

Answer 27

You need to make it equal 0
/-4x
X^2-4x-12=0
(X-6)(x+2)=0

Question 28

Solve 5x +y =21

3x-y=11

Answer 28

5x+y=21
Plus 3x-y =11
= 8x = 32
X=4

Sub x=4 into A
5x+y=21
5x4+y=21
20+y=21
Y=1

Question 29

Solve 3x +2y=8

4x+y=14

Answer 29

Make sure you have the same number of y’s

3x+2y=8
4x+y=14 /x2/ 8x+2y=28

3x+2y=8
3x4+2y=8
12+2y=8
2y=-4
Y=-2

Question 30

Solve 3x-2y=-2

5x+5y=30

Answer 30

3x-2y=-2 /x5/ 15x-10y=-10
5x+5y=30 /x2/ 10x+10y=60

15x-10y=-10
Plus 10x+10y=60
=25x=50
X=25

Sub x=2 into 3x-2y=-2
3x2-2y=-2
6-2y=-2
/-6
-2y=-8
/divide by 2
Y=4

Question 31

6 pencils and 2 crayons cost £2.70. 5 pencils and 3 crayons cost £2.45. How much is the cost of a pencil and the cost of a crayon?

Answer 31

A: 6p+2c=2.70 /x3/ 18p+6c=8.10
B: 5p+3c=2.45 /x2/ 10p+6c=4.90

18p+6c=8.10
Take away 10p+6c=4.90
=8p=3.20
/divided by 8/
P=0.40
1 pencil costs 40pence

Sub p=0.40 into A or B
5p+3c=2.45
5x0.40+3c=2.45
2+3c=2.45
2+3c=2.45
3c=0.45
C=0.15
Cost of crayon is 15 pence