Solving Equations Flashcards
Solve 3x-4=11
3x-4=11 (+4 to both sides) 3x=15 (Divide by 3) X=5
Solve 3x/4 -1 =10
3x/4 -1 = 10 (+1) 3x/4=11 (X4) 3x=44 (Divide by 3) X=44/3
Solve 5-2x=10
5-2x=10 (-5) -2x=5 (Divide by 2) X=-5/2 X=-2.5
Solve 3(2x-5)=10
6x=-15=10 /+15 6x=25 /divided by 6 X=25/6 =4 1/6
Solve 12=3(4x+1)+2
12=3(4x+1)+2 12=12x+3+2 12=12x+5 /-5 7=12x /divide by 12 7/12=x
Solve 5-2(3x-4)=10
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
Solve 4x -3 = 2x+1
/-2x 2x-3=1 /+3 2x=4 (Divide by 2 X=2
Solve 6-3x=8x+2
/+3x 6=11x+2 /-2 4=11x /divide by 11 4/11=x
Solve 3x -2 = 10- 8x
/+8x 11x-2=10 /+2 11x=12 /divide by 11 X=12/11
Solve 3(2x-1)=2(4-5x)
6x-3=8-10x /+10x 16x=11 /+3 16x=11 /divided by 16x X = 11/16
Solve 2(5y-1)=3(2y+1)-4
10y-2=6y+3-4 10y-2=6y-1 /-6y 4y-2=-1 /+2 4y=1 Y=1/4
Kevin thinks of a number then adds 7. His answer is 19. Work out the number Kevin is thinking of.
x +7=19
/-7
X=12
a) write an expression, in terms of x, for the sum of the angels of this triangle
X \ \ \. \ \\_\_\_\_\_2x_\ ^2x+90*
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*
Solve 16-x/4 =1-x
/x4 16-x = 4-4x /+4x 16+3x=4 /-16 3x=-12 /divided by 3 X=-4
Solve 2x-1/2 - x-5/3 =5/4
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
How do we work out the square root of a negative number?
We don’t, it’s impossible
What does it mean for something to be quadratic?
It has an x^2
Solve x^2+5x+6=0
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
What’s special about a solving a quadratic answer?
It has two answers
Solve x^2-7x+12=0
(X-3)(x-4)=0
X=3 or x=4
Solve x^2-8x+17=2
/-2
X^2-8x+15=0
(X-5)(x-3)=0
X=5 or x=3
What is the rule for dividing by an unknown?
Don’t
Solve x^2 = 4x+12
You need to make it equal to 0 /-4x X^2-4x=12 /-12 X^2-4x-12=0 (X-6)(x+2)=0
Solve: 2x^2 + 11x + 12 = 0
(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
Solve 3x+2y=13
5x+2y=19
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
Solve 4x +3y=8
6x+3y=9
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
Solve x^2=4x+12
You need to make it equal 0
/-4x
X^2-4x-12=0
(X-6)(x+2)=0
Solve 5x +y =21
3x-y=11
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
Solve 3x +2y=8
4x+y=14
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
Solve 3x-2y=-2
5x+5y=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
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?
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
