Solving Equations and Word Problems
Solve: x/3 - 7 = 5
x = 36
Simplify: x2 * x10
x12
Factor: n2 -5n + 6
(n - 3)(n - 2)
Simplify: (x2 - 4)/(x2 - 7x - 18)
(x - 2)/(x - 9)
Simplify: 3 lb : 2 oz
24 : 1
Solve: 5n = 8n - 18
n = 6
Multiply: (4x - 3)(x - 4)
4x2 - 19x + 12
What are the six types of factoring?
GCF, difference of squares, trinomial, trinomial a > 1, perfect squares, grouping
What must you always do before you begin canceling when simplifying an algebraic fraction?
Factor!
Solve: (6x - 2)/7 = (5x + 7)/8
x = 5
Solve: 3(a - 5) + 19 = -2
a = -2
4x2 - 3y + 13
Factor: m4 - 25y2
(m2 + 5y)(m2 - 5y)
Why do problems with algebraic fractions need domain restrictions?
Fractions are divisions of numerator by denominator. Since we cannot divide by zero, the denominator of a fraction cannot equal zero.
The sides of a triangle are in the ratio 3:5:6. The perimeter is 98 cm. Write an equation and find the sides.
Equation: 3x + 5x + 6x = 98
Sides: 21 cm, 35 cm, 42 cm.
The sum of 4 consecutive integers is 84. Write an equation and find the numbers.
Equation: x + x+1 + x+2 + x+3 = 84
Numbers: 19, 20, 21, and 22
Simplify: (-3x2yz3)3
-27x6y3z9
Factor: 3a3 + a2 - 6a - 2
(a2 - 2)(3a +1)
Divide x/(x2 - 36) by 2/(5x - 30)
Solve: 4/y - 1/4 = 1/12
y = 12
I have twice as many nickels as quarters. If my coins are worth $4.90 total, how many quarters are there?
14 quarters.
Simplify: (n + 4)2
n2 + 8n + 16
Factor: 3x3 + 15x2 - 108x
3x(x + 9)(x - 4)
Subtract: 3/(y - 6) - 1/y
(2y + 6)/y(y - 6)
Solve: 4/(x + 1) - 1/x = 1
x = 1