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What are the additive and multiplicative inverses of -√3
PEMDAS!!
1. Which expression is not equivalent to the others?
a. 3x - y - x - y
b. -2(x - y)
c. 2(x - y)
d. 2x - 2y
2. Evaluate the expression |x + 3| - |x - 6| + |x| for x = -2
3. Simplify by combining like terms:
Solve for x (state any restrictions on variables)
1.
2.
3.
Inequalities
1. 11 < 3y + 2 < 20
9 < 3y < 18
3<y<6
3. -3x + 1 > 4 and -9 < 5x + 1 < 6
-3x > 3
x < -1
2. 6b + 3 < 15
6b < 12
b<2
4b - 2 > 18
4b > 20
b>5
4. Write an inequality for the following graph
-10 < 5x < 5
-2 < x < 1
-2
combined solution:
-2 < x < -1
or
-1
From yesterday's assessment
1. 8x-5 ≤ -4(-2x-3)
8x-5 ≤ 8x+12
-8x -8x
-5 ≤ 12 true
x = all real numbers
(-∞, ∞)
2. -2(3x+1)-6 > 2(2x+7)+6
-6x-2 -6 > 4x+14 +6
-6x-8 > 4x +20
-10x > 28
x < 28/-10
x < -14/5
(-∞, -14/5)
3. 2(3x-7) ≤ 22 and -5x+16 > 1/2 (2x -8)
6x-14 ≤ 22
-5x+16 > x-4
6x ≤ 36
x≤6
10/3
(-∞, 10/3)
20 > 6x
>x
4. 5-4(x+6) > 3x+2
5-4x-24 > 3x+2
-4x-19 > 3x+2
-7x > 21
x < -3
or
-2x+7 ≥ -(8x+3)
-2x+7 ≥ -8x-3
6x ≥ -10
x ≥ -5/3
combined: (-∞,-3)∪[-5/3,∞)
5. 6x + 14 ≤ 2x - 5 ≤ 7
combined: (-∞,-19/4]
like writing 6x+14 ≤ 2x-5 AND 2x-5 ≤ 7
4x ≤ -19
2x ≤ 12
x ≤ -19/4
x≤6
Absolute Value
step 1 : isolate the absolute value
step 2: set up two equations/inequalities (one straight up with
out the absolute value, the other switch the sign and inequality)
step 3: solve each side
step 4: when necessary, check for extraneous solutions
From assessment:
7. 2/3|3x-4| = 6x + 2
8. 3|4x-1|+13 = 7
(3/2)* 2/3|3x-4| = 6x + 2 *(3/2)
3|4x-1| = -6
|3x-4| = 9x+3
|4x-1| = -2
3x-4 = 9x+3
3x-4 = -9x-3
-6x = 7
12x = 1
4x = -1
4x = 3
x = -7/6
x = 1/12
x = -1/4
x = 3/4
Check!
4x-1 = -2
4x-1 = 2
Absolute Value Inequalities
10. 5|2x+9| + 10 > 7
5|2x+9| > -3
|2x+9| > -3/5
2x+9 > -3/5
10x+45 > -3
or
2x+9 < 3/5
10x+45 < 3
10x > -48
10x < -42
x > -48/10
x < -42/10
combined x >-24/5 or x <-21/5
note: make the math
friendlier by getting rid
of the fraction
12. |x+1| ≤ 6 or |2x-2| ≥ 18
|x+1| ≤ 6
|2x-2| ≥ 18
x+1 ≤ 6 and x+1 ≥ -6
2x-2 ≥ 18
or
2x-2 ≤ -18
x ≤ 5 and x ≥ -7
2x ≥ 20
or
2x ≤ -16
or
x ≤ -8
x ≥ 10
Write the combined inequality as a single absolute value inequality
-16 ≤ x ≤ 36
Probability
P(event) =
event
sample space
For example, choosing from a deck of 52 cards. (note there are four
suits that include the numbers 2-10, an ace, jack, queen and king.)
P(ace) =
P(jack of spades) =
P(red card) =
Experimental Probability and Simulations
Using rand on your calculator
example, drawing 5 cards
P(at least 3 red) =