Part A
1. 14k+k<30
Add the left hand side to get;
15k<30
Divide both sides by 15.
[tex]\frac{15k}{15}\:<\:\frac{30}{15}[/tex]
k<2
2. We have 9d-3d+7>31
Group similar terms to obtain:
9d-3d>31-7
Combine similar terms:
6d>24
Divide both sides by 6
[tex]\frac{6d}{6}\:>\:\frac{24}{6}[/tex]
This implies that:
d>4
3. We have 13x-2x>77
This implies:
11x>77[tex]\frac{11x}{11} \:>\:\frac{77}{11}[/tex]
x>7
4. We have 5y<7y+18
This implies
5y-7y<18
-2y<18
Divide both sides by -2 and reverse the sign.
[tex]\frac{-2y}{-2} \:>\:\frac{18}{-2}[/tex]
[tex]y\:>\:-9[/tex]
5. The given expression is;
3f-12>-10+9f
Group similar terms:
-12+10>9f-3f
-2>6f
Divide both sides by 6.
[tex]\frac{-2}{6}\:>\:\frac{6f}{6}[/tex]
[tex]-\frac{1}{3}\:>\:f[/tex]
[tex]f\:<\:-\frac{1}{3}[/tex]
6. We have 4t-8<2t-2
Group similar terms;
4t-2t<-2+8
2t<6
t<3
7. We have
15h+16>6h-20
Group like terms;
15h-6h>-20-16
9h>-36
Divide both sides by 9
h>-4
8. The given inequality is
4r-2r>6-r
This implies
4r-2r+r>6
3r>6
r>2
Part B
x-27=193
x=193+27
x=220
2. The given equation is
f(12)=48
or
12f=48
f=48/12
f=4
3. We have the equation 4s+2=74
4s=74-2
4s=72
s=18
4. The given equation is
9(r+1)-18=2r+12
Expand to get:
9r+9-18=2r+12
Group like terms:
9r-2r=12+18-9
7r=21
r=3
