Texas Success Initiative (TSI) Lone Star College（德州成功倡议(TSI)孤星大学）.pdf

Texas Success Initiative (TSI) MATH REVIEW Algebra Review ALGEBRA FUNCTIONS Variables and Algebraic Expressions  The sum of a number and 5 means: m + 5 or 5 + m  The number diminished or subtracted by 7 means: m – 7  Ten times a number means: 10m  z divided by 3 means: z / 3 Algebraic Expressions  Key words which denotes addition sum, plus, greater than, more than, larger than, rise, increase, gain  Key words which denotes subtraction difference, minus, less than, smaller than, fewer than, decrease, drop, reduce, diminish, lose  Key words which denotes multiplication multiplied by, times, product, twice  Key words which denotes division quotient, divided by, ratio, half Solving Equations Examples:  If 3t – 7 = 5t, then 6t = ? Solve for t; then find 6t 3t – 5t = 7 - 2t = 7 t = - (7 / 2) Thus, 6t = 6(-7/2) = -21 Solving Equations Examples:  If (x-1)/x =20, then x = ? x-1 = 20x x-20x = 1 -19x = 1; thus x= -1/19 Ratios Proportions  Ratio is a way of comparing two or more variables.  It is written as a:b or a/b  Proportions are written as two ratios in terms of fractions equal to each other. Ex Solve this proportion for s: p is to q as s is to t p/q = s/t s = t(p/q) Solving Equations Examples:  Variables x and y are directly proportional, and y=2 when x=3. What is the value of y when x=9? y ∝x y = kx where k is a constant 2 = k(3) ; k= 2/3 y=(2/3)x Now, we can substitute x=9 and find y: y = (2/3) 9 = 6 Solving Equations Word Problem:  A group of people ordered soup and sandwiches for lunch. E