Solving Equations
Add 5 to both sides (inverse operations)
When graphing inequalities, when do you used an open circle on the number line.
When x is not equal to the number given (when it is strictly < or >)
Solve for x.
x + 3 < 17
x < 14
What does applying the absolute value to something do to it?
The absolute value forces all values to be positive.
When |x| < some negative number, how many solutions are there?
No solutions.
What is the inverse operation for each of the following operations:
Addition
Division
Subtraction & Multiplication
Should ∞ always be paired with a parenthesis or brackets? Why?
Parenthesis. X can never be exactly equal to ∞.
Solve for x.
2x + 4 > 16
x > 6
What is |-18|?
18
When |x| > some negative number, how many solutions are there?
All real numbers (all solutions)
Solve for x.
7x + 8 = 85
x = 11
Write x > 8 in interval notation.
(8,∞)
Solve the inequality, write your solution in interval notation:
x + 7 + 2x < 19
x < 4
(-∞, 4)
Solve for x. Note how many solutions you get.
|x+3|=0
x = -3
One solution
Solve for x. Write your answer in interval notation.
|x + 3| + 5 > 5
x > -3
(-3, ∞)
Solve for x.
x/3 + 7 = 13
x = 18
Write x<10 or x>19 in interval notation.
(-∞, 10)u(19, ∞)
Solve the following inequality, write your answer in interval notation:
12 -5x + 5 < 57
x > -8
(-8, ∞)
Solve for x. Note how many solutions you get.
|-3x + 9| = 33
x = -8 and x = 14
Two solutions
Solve for x. Write your answer in interval notation.
|4x + 7| - 8 < 27
x < 7
x > -10.5
(-10.5, 7)
Solve for x.
x/3+20 = 4(3x - x)
x = 60/23 or about 2.6
Write x<10 and x>-6 in interval notation.
(-6, 10)
Solve for x. Write your answer in interval notation.
-0.5x - 5 -3x > 16
x < -6
(-∞, -6)
Solve for x. Note how many solutions you have.
|3x + 7| + 7 = 4
No solutions
Solve for x. Write your answer in interval notation.
|-0.5x + 7| - 8 < 16
x > -34 x < 62
(-34, 62)