More Equations with Rationals

More Equations with Rationals

Goal: To learn how to solve equations with fractions

Example 1: Solve the following equations.

a) 4=-23p-2
LCD(1,3)=3
34=3-23p-2
12=-2p-2
12=-2(p)-2(-2)
12=-2p+4
2p=4-12
2p=-8
2p2=-82
P=-4
The solution is p=-4

b)w-14=w+23
LCD(3,4)=12
12 ×w-14=12 ×w+23
3(w-1)=4(w+2)
3w-3=4w+8
3w-4w=8+3
-w=11
-1w-1=11-1
W=-11

OR

w-14=w+23
3(w-1)=4(w+2)
3(w-1)=4(w+2)
3w-3=4w+8
3w-4w=8+3
-w=11
-1w-1=11-1
W=-11

c) u-32-2=3u2+2u+15
LCD(2,5)=10
10u-32-2=103u2+2u+15
5(u-3)-20=5(3u)+2(2u+1)
5u-35=19u+2
5u-19u=2+35
-14u=37
-14u-14=37-14
u=-3714or u =-3514
u=-3714 is the solution

d) 35x-2=-23x+4+15
LCD3,5=15
15 ×35x-2=15 ×-23x+4+15
15 35(x-2)=15-23x+4+1515
33x-2=5-2x+4+3
9(x-2)=-10(x+4)+3
9x-18=-10x-40+3
9x-18=-10x-37
9x+10x=-37+18
19x=-19
x=-1