Download Notes Module 2

Notes Module 2
Equations and Proportions
Notes: Module 2.01 – One Step Equations
• 1st  Simplify each side: distribute & combine like terms
• 2nd  If you have variables on both sides, you must add or
subtract one of them to move it so you will only have a
variable on one side
• 3rd  Focus on the side with the variable. Add or subtract
the number without the variable
• 4th  Divide or multiply by the coefficient to get the variable
alone
• Note: the variable can NOT be negative (you have to multiply
by -1 on both sides to get rid of the negative)
Examples
3x – 5 = 7
+5 +5
3x = 12
3 3
x=4
6x + 23 = 27 – 2x
+ 2x
+ 2x
8x + 23 = 27
- 23 -23
8x = 4
8 8
x = 4/8 or ½
2 (x + 8) – 9 = 5
2x + 16 – 9 = 5
2x + 7 = 5
-7 -7
2x = -2
2 2
x = -1
Notes: Module 2.02 – Multi-Step Equations
• Consecutive Integers Problems
Regular consecutive integers
Odd or Even Consecutive Integers
Term number
How to solve
Term number
How to solve
1
X
1
X
2
X+1
2
X+2
3
X+2
3
X+4
4
X+3
4
X+6
• Example: Find three consecutive integers whose sum is 18.
(x) + (x + 1) + (x + 2) = 18
3x + 3 = 18
x=5
-3 -3
3x = 15
3
3
Term 1: x  5
Term 2: x + 1  5 + 1 = 6
Term 3: x + 2  5 + 2 = 7
Answer: 5, 6, 7
Notes: Module 2.02 – Multi-Step Equations
• Absolute Value Equations
• Will always have 2 answers!
• 1st  Get the absolute value info on one side and everything else on the other
• 2nd  Set up two equations, each with the expression from the absolute value bars. Set
one equal to the original number, and set the other equal to the negative (or opposite)
of the original and solve both equations.
• Example: |x + 4| - 3 = 10
+3 +3
|x + 4| = 13  x + 4 = 13 &
x + 4 = -13
-4 -4
-4
-4
x=9
&
x = -17
• Note: Absolute values can never equal a negative number
• |x| = -(#) then no solution
Notes: Module 2.03 – Literal Equations
• Solving for a specific variable
• These equations have several variables, but you only focus on the one they
tell you. Move the others just how you would (opposite PEMDAS), you just
don’t actually work out and solve for a number.
• Examples:
Solve for ‘r’ 4qr+2t=7u
Solve for ‘y’ xy+w=p
-2t -2t
-w -w
4qr=7u-2t 
xy=p-w  y= p-w
4q
4q
x
x x
r = 7u-2t
4q
Notes: Module 2.05 – Problem Solving
• In order to solve word problems, you need to
use one of several tools:
• Make a table to organize the information
• Create and equation and solve
• Figure out which value is changing and which value is
constant
• Make sure you write the equation with a variable AND
solve for the variable
Notes: Module 2.06 – Proportions
• Proportion is two ratios that equal each other (remember: you can’t
have a zero in the denominator of either ratio)
• In a proportion, the cross products are equal
• Percent problems are always out of 100 (meaning the percent is the
numerator and 100 will always be the denominator)
• Percent of increase or decrease
Notes: Module 2.07 – Solving Inequalities
• Inequalities usually have a solution that is more than one number
• Closed circle (≥ or ≤) means the number is included (greater/less than or equal
to)
• Open circle (> or <) means the number is NOT included (greater/less than
• Solve an equality the same you would solve an equation, except when
multiplying or dividing by a negative number **you flip the inequality sign**
• ‘And’ problems find the solutions that are in common; solutions should go toward
each other and stop at each end
• ‘Or’ problems find what the solutions are for either inequality; usually going away
from each other, but if going towards each other, the solution is ‘all real numbers’
Notes: Module 2.07 – Solving Inequalities (con.)
• Absolute value inequalities