1styear Solving Equations
From last chapter
Multiplying terms with Brackets and Simplifying
Eg. -4(x-1)+2(x-8)Multiply everything outside by what`s inside brackets including signs
-4x + 4+ 2x- 16Tidy up terms that are the same eg. -4x+2x=-2x, +4-16=-12
-2x-12
Follow the steps to solve
- Multiply out brackets
- Put x`s on the left of the equals & numbers on the right(anything moves sides it changes sign)
- Tidy up x`s and tidy up numbers
- To get x on its own you ÷ whatever is stuck to it into the other side.
Example:
5x - 3= 17x`s on left numbers on right move -3 and becomes+3
5x = 17+3tidy up numbers-- 2 same signs add and keep sign
5x = 20to get x ÷ 5 into 20
x = 20
5To get x on its own you ÷ whatever is stuck to it into the other side
x = 4
Example:
4x-2 = 5x -5x`s on left changes to -5x numbers on right move -2 and becomes+2
-5x+4x = -5+22 different signs subtract and keep sign of bigger number
-1x = -3
X = -3Toget x on its own you ÷ whatever is stuck to it into the other side
-1
X = 3
Example:
5x-2(3-x) = 2(x+2)Multiply out brackets
5x -6 +2x = 2x+4x`s on the left, numbers on the right
5x+2x-2x =4+6Tidy up x`s and tidy up numbers
5x =10
X =10To get x on its own you ÷ whatever is stuck to it into the other side
5
X=2
Example:
3(x-5)-2(1-x) =3-3(4-x)Multiply out brackets
3x -15-2+2x =3-12+3xx`s on the left, numbers on the right
3x+2x-3x=3-12+15+2Tidy up x`s and tidy up numbers
2x = 8
X = 8To get x on its own you ÷ whatever is stuck to it into the other side
2
X= 4
Example:
-3(x-1)+5=2(x+1)-3(5x-1)+13 Multiply out brackets
-3x+3+5 =2x+2-15x+3+13x`s on the left, numbers on the right
-3x-2x+15x = -3-5+2+3+13Tidy up x`s and tidy up numbers
10x = 10
X= 10To get x on its own you ÷ whatever is stuck to it into the other side
10
X = 1
Example:
11 =7(x+1)-2(3-8x) -3xMultiply out brackets
11 = 7x+7 -6 +16x -3xx`s on the left, numbers on the right
-16x-7x +3x =-11+7-6Tidy up x`s and tidy up numbers
-20x = -10
X = -10To get x on its own you ÷ whatever is stuck to it into the other side
-20
X = + 1 or 0.5
2