MTH111
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The variable x increased by 6
x + 6

The variable x decreased by 6
x  6


5 more than 3 times the variable x
3x + 5

7 more than the square root of the variable x

items are in the square root box x + 7

2 less than the product of four and a number
4x  2

The sum of 7 divided by a number and that number divided by 7
7/x + x/7

The product of 6 and a number increased by 4 is 35
6(x + 4) = 35

One less than the products of 12 and a number
12x  1

Words meaning Addition
 plus
 sum
 more than
 increased by

Words Meaning Subtraction
 minus
 difference
 less than
 decreased by

Words Meaning Multiplication
 times
 product
 twice
 multiplied by

Words Meaning Division
 divided
 quotient
 ratio
 divided by

=
 equals
 gives
 is
 will be
 yields
 is the same as
 was


Solution
value of the variable that makes the equation true

Evaluate XY/3 when x is 10 more times than 2 times y and y = 8
 x = 2y +10
 x = 2(8) + 10
 x = 16 + 10
 x = 26
 268/3 =
 18/3 =
 6

If 10 is decreased to 3, the decrease is what % of the original number
 Formula A=P * B
 A=decrease
 P =%
 B = Original Amount
 10  3 =7
 A=P * B
 7=P *10
 7/10 = P*10/10
 multiply = answer 70
 turn into percent.
 Answer 70%


Inequalities
15 + 5 ≥ 7(2x +) +9
15 + 5 ≥ 14x + 7 + 9
15x – 14x ≥ 7 + 9 – 5
X ≥ 16 – 5
X ≥ 11 [11, ∞)

The angels measuure is 20 degrees more than triple its supplement
 x = 20 + 3(180x)
 x= 20 + 540  3x
 x+3x = 20+540
 4x=560
 answer = 140

Inequality symbols
 ( ) parenthesis are NOT included in interval notation
 [ ] square brackets are inculded
 ( ) parenthesis are always included with  infinity or positive infinity

Complementary Angle
 90 degrees
 70 degree and 20 degree are complementary
 to find the measurement of the complement subtract the given angle from 90 degrees.
 (i.e. a angle is 25 degrees)
 90  25 = 65 degrees

Supplementary Angle
180 degrees

One angle of a triangle is three times as large as another. the measure of the third angle is 65 degrees more than that of the smallest angle. find the measure of each angle.
x + 65
 x + 3x + (x + 65)=180
 5x + 65 = 180
 5x = 180  65
 5x = 115
 x = 23 (smallest angle)
 The measure of the angle that is three times as large as the smallest angle is 3x
 3x = 3 * 23 = 69 degrees
 The measure of the angle that is 65 degrees more than the smallest angle is x + 65
 x + 65 = 23 + 65
 x + 65 = 88
The three angles aer: 23 + 69 + 88 = 180 degrees

The measurement of the angles supplmenet is 80 degrees more than three times that of it's complement
complement 90  x
supplement 180  x
 180 x = 80 + 3 * 90  x
 180 x = 80 + 3(90  x)
 180  x = 80 + 270  3x
 180  x = 350  3x
 180  x + 3x = 350
 180 + 2x = 350
 2x = 350  180
 180 + 2x = 170 (divide)
 x = 85

Find the measure of the complement of a 37 degree angle
Two angles are complementary if and only the sum of their measure is 90 degrees
90  37 = 53 degrees

Measure the supplement of a 117 degree angle
two angels are supplementary if and only their sum measures 180 degrees
180  117 = 63 degrees

Linear inequality symbols
 ≤  less than or equal to
 <  less than
 ≥  greater than or equal to
 >  greater than
 ∞  infinity

In a triangle, the measure of the first angle is three times the measure of the second angle. The measure of the third angle is 20 degrees less than the second angle. What is the measurement of each angle?
 x + y + z = 180
 3y + y + y20 = 180
 5y  20 = 180
 5y = 180  20
 5y = 200
 y = 40
x = 3 * 40 = 120 z = 40  20 = 20

Inconsistent equation
 x = x + 4
 use "no solution" or o

Identity
An equation that is true for all real numbers
x + 3 = x + 2 + 1

formulas using letters only for C
 C + M + S (isolate the C)
 C + M  M = S  M
 C = S  M

Exponents
2^4
when there is a negative , even will always result in a positive result whereas a odd number will always result in a negative

Rectangle  Perimeter and Area

Square  Perimeter and Area

TRIANGLE Perimeter and Area

PARALLELOGRAM Perimeter and Area

Trapezoid Perimeter and Area
 P = B1 + B2 + A + C (the one and two are small and on the bottom of the letter)
 A= 1/2H(B1 =1B2)
B= BASE 1 AND BASE 2

Circle circumference and Area
 C = PIE (3.14)D OR C = 2(3.14)R
 A= 3.14(R^2)