Hwk: Pg. 200:
#6.
a) If x is the supple montary angle of y, then y=2x.
x+y=180
x+2x=180
3x=180
3xx=1803
x=60
y=2x
=260
=120
The angles are 60 and 120
b)Similarly, x+5x=180
x=30and 5x=150
#7. X+2x+3x=90
#9. 8-13w-2=-5w-3-14w-3
8-(3w)-(-2)=-5(w)-5(-3)-(4w)-(-3)
8-3w+2=-5w+15-4w+3
10-3w=-9w+18
-3w+9w=18-10
6w=8
6w6=86
w=43
Solving Equations with Fractions
Goal: To learn how to solve equations with Fractions.
Example: Solve the following equations.
a) x+53=-2
x+53=-21 Multiply both sides by the LCD
LCD(3,1)=3Simplify
3xx+53=3x-2 Move +5 to the right side
x+5=-6
x=-6-5
x=-11
The solution is x=-11
b) y+25=y-23
LCD(5,3)=15
15y+25=15y-23 Multiply by the common denominator
3(y+2)=5(y-2) Expand
3y+6=5y-10 Transpose the variable term
3y+6-5y=-10 Simplify
-2y+6=-10 Transpose the constant term
-2y=-10-6 Simplify
-2y=-16 Divide by the coefficient
-2y-2=-16-2
Y=8
Or
y+25=y-23
3(y+2)=5(y-2)
Simplify and solve
c) 152n+1=23n-1
LCD(5,3)=15
15152n+1=1523n-1
3 ×1 ×2n+1=5 ×2 ×n-1
3(2n+1)=10(n-1)
3(2n)+3(1)=10(n)-10(1)
6n+3=10n-10
6n-10n=-10-3
-4n=-13
-4n-4=-13
n=134 or n=314
The solution is n=134
d) ½k-23k+7=34k
LCD(2,3,4)=12
1212k-23k+7=1234k
1212k+12-23k+127=33k
6k+4-2k+84=9k
6k-8k+84=9k
-2k+84=9k
-2k-9k=-84
-11k=-84
-11k-11=-84-11
k=8411 or k=7711
The solution is k=8411
