LAGUARDIA COMMUNITY COLLEGE
Department of Mathematics, Engineering, and Computer Science
MAT96 ELEMENTARY ALGEBRA
ALEKS PILOT
LAB # 3
Name: ____________________________________
Date: ____________________
Instructor: _________________________________
Section: __________________
You need to show all work. Indicate the right answer in the answer sheet. Even if you mark the
right answer, but do not show work on this sheet, you will not be given credit for that question:
Tutor problems are the examples for the unsolved problem(s) that follow them.
1. (Tutor) Solve the equation: 5  4  p   3 3 p  9   9
Solving Linear Equations Involving Multiple Steps
To solve an equation requiring multiple steps:
1. Simplify both sides of the equation.
2. Apply the addition or subtraction property of equality to collect the variable terms on one side of the
equation.
3. Apply the addition or subtraction property of equality to collect the constant terms on the other side of
the equation.
4.Use the multiplication or division property of equality to get a coefficient of the variable term equal to 1.
Solution:
5(4  p)  3(3p  1)  9
20  5p  9 p  3  9
20  5p  9 p  12
20  5p  5p  9 p  5p  12
20  4 p  12
20  12  4 p  12  12
32  4 p
32 4 p

4
4
8 p
Spring 2014
Clear the parentheses
Add like terms on the right
Subtract 5p from both sides
Add 12 to both sides
Divide both sides by 4
The solution is p = 4
2. Solve the equation: 17  s  3  4  s  10  13
3. (Tutor) Solve the equation:
1
1 1
3
 3m  4   m 
4
5 4
10
Note: To solve an equation by first clearing fractions, multiply both sides of the equation by the
LCD of all terms in the equation.
Solution:
1
1 1
3
(3m  4)   m 
4
5 4
10
1
1
1
3
20  (3m  4)    20  m  
5
10 
4
4
5(3m  4)  4  5m  6
15m  20  4  5m  6
15m  24  5m  6
15m  5m  24  5m  5m  6
10m  24  6
10m  24  24  6  24
10m  30
10m 30

10 10
m3
Spring 2014
The LCD of
1 1
3
, and
is 20
4 5
10
Apply the distributive property
Clear the parentheses
Combine like terms
Subtract 5m from both sides
Subtract 24 from both sides
Divide both sides by 10
The solution is m = 3
4. Solve the equation:
1
1
 4n  3   2n  1
12
4
5. (Tutor) Solve the equation: 0.04  y  10  0.06  y  2  2
Note: When clearing decimals in an equation, multiply both sides by a convenient power of ten.
Solution:
0.40( y  10)  0.60( y  2)  2
10 0.40( y  10)  0.60( y  2)  10 2

 
4 y  10  6 y  2  20
4 y  40  6 y  12  20
2 y  28  20
2 y  28  28  20  28
2 y  8
2 y 8

2 2
y4
The solution is y = 4
Spring 2014
Multiply both sides of the equation by 10
Multiply both sides of the equation by 10
Apply the distributive property
Combine like terms
Subtract 28 from both sides
Divide both sides by -2
6. Solve the equation: x  4  2  0.4 x  1.3
7. (Tutor) Solve the inequality and graph the solution: 2 x  7  5( x  4) ,
Solution:
(Using distributive property)
(Simplifying)
(Dividing by -3 ) Note that dividing by a negative number reverses the inequality
Graphically, the solution set can be represented as
9
8. Solve the inequality and graph the solution: 3(2 x  4)  2( x  1)
Spring 2014
9. (Tutor) Solve the equation for y;
Solution: Since the variable is y, we first isolate the term containing y;
(Keeping term in y by itself)
(Dividing both sides by 5 to isolate y)
Or
10. Solve the equation for w;
11. (Tutor) Set-Builder Notation
Solutions:
Inequality: x  2
Set-builder notation:
x | x  2
The set of all x such that x is greater than or equal to 2
Interval Notation
Inequality: x  4
Spring 2014
Interval Notation:  4
,

Inequality: x  3
Interval Notation:
 
,
3
12. Solve the inequality. Graph the solution set and write the set in interval notation: 8  2 x  10
Extra Practice Problems (Optional)
1. Solve the equation for the variable
2. Four times a number is the same as the sum of twice a number and ten. Find the number.
3. Solve the inequality and graph the solution :
4. Translate the English phrases into mathematical inequality: The temperature in the classroom, t,
was at most 75 F .
5. Solve for x:
Spring 2014