05b More Rearranging and Solving Equations
Today is nothing new, but lots of practice. Rearranging equations is a skill that will come up time and
time again in Maths (and Physics and Chemistry, if you’re heading that way) so you need to do lots of
practice to get confident in these skills
Simple rearrangements – Remember the Golden Rule Treat both sides of the equation equally
Rearrange to make x the subject
1.
2.
3.
4.
5.
y=x−7
y = 2x − 7
y = 3x + 9
y = 7 − 2x
y = x/5
Make v the subject.
1. w = 3v,
2. w = 1/3 v
3. w = v/3
4. w = 2v/3
5. w = 2/3 v
Rearrange to make the unknown the subject of the equations (ie x=?) , then solve for x
1. 25=4x-3
2. 16=4/3x +4
3. 60=5(x+4)
4. 88= t+54
5. 22x= 55x 0.2
Order of Operations – AKA Using BEDMAS
Brackets – Exponents – DIvision – Multiplication – Addition - Subtraction
1. 8 + 9 – 7 =
2. 15 × 13 + 25 × 6 =
3. 25 - 10 + 9 =
4. (16 × 9) × 15 =
5. 12 + (6 ÷ 2) =
6. 21 + 4 × 12 =
7. 16 ÷ 2 + 3 =
8. 12 ÷ 2 × (8 ÷ 2) =
9. 8 ÷ 2 × 24 =
10. 20 + (12 × 19) =
Substituting into equations
What is y when x =3, or x=-9
1.
2.
3.
4.
5.
Y=4x+5
Y=3x-7
Y=x/3 +6
Y=x2 - 4
Y=x/2+ 6
ANSWERS
1.
2.
3.
4.
5.
X=Y+7
X=(y+7)/2
X=(y-9)/3 or x= y/3 -3
X= (y-7)/-2
X=5y
1.
2.
3.
4.
5.
V=w/3
w=3w
V=3w
V=3w
V=3w/2
When x=3
1.
2.
3.
4.
5.
17
2
7
5
7.5
BEDMAS
1.
2.
3.
4.
5.
6.
7.
8.
9.
10,
345
24
2160
15
69
11
24
96
10.
248
When x=-5
1.
2.
3.
4.
5.
-31
-28
-3
77
-1.5