solving equations and inequalities

Question 1

solve for z. two step equation with decimals

-z/0.6-0.5=-6.5
+0.5 +0.5

-z/0.6=-6
0.6(z/-0.6)=(-6)(-0.6)

Answer 1

z=3.6

Question 2

Solve for z. Express your answer as a proper or improper fraction in simplest terms.

-1/2=-7/8-1/4z
+7/8 +7/8+
1/2+7/8=1/4z
-1/2x4/4+7/8=-1/4z
-4/8+7/8=-1/4z
3/8=-1/4z
(-4/1)(3/8)=(-4/1)(-1/4z)

Answer 2

-12/8=z
-3/2=z
-1.5=z

Question 3

two step equations with fractional coefficients, solve for a

12+5/8a=27
-12 -12
5/8a=15
(8)(5/8)a=(15)(8)
5a=120
5a/5 =120/5

Answer 3

a=24

Question 4

two step equations with fractional coefficients, solve for y Express your answer as a proper or improper
fraction in simplest terms.

-1/4+1/6y=-1/6
+1/4 +1/4
1/6=-1/6+1/4
1/6y=-1/6x2/2+1/4x3/3
1/6y=-2/12+3/12
1/6y=1/12
(6/1)(1/6y)=(1/12)(6/1)

Answer 4

y=6/12
y=1/2

Question 5

linear inequalities, solve the following inequality for s, write answer in simplest form

8s+8<s+9
-s -s
7s+8<9
-8 -8
7s<1
7s/7<1/7

Answer 5

s<1/7

Question 6

linear inequalities with fractions, solve the following inequality

-1+1/2x<-(-3/2x+1)-9
-1+1/2x<3/2x-1-9
1/2x-1<3/2x-10
+1 +1
1/2x<3/2x-9
-3/2x -3/2x
-x<-9
-x/-1>-9/-1

Answer 6

x>9

Question 7

absolute value equations, solve for all values of x in simplest form

17=/11-2x/

17=11-2x -17=11-2x
-11 -11 -11 -11
6=-2x -28=-2x
6/-2=-2x/-2 -28/-2=-2x/-2

Answer 7

-3x
14x