Test 1
(42-23) * (15-32)
-64
The absolute value of a negative number is always what type of number?
Any absolute value is a POSITIVE number.
Write an inequality & solve:
The difference of a number and 10 is at most -1
x - 10 <= -1 ... x <= 9
What type of inequality goes with |x|>7
it would be an "OR" ... since the values further away from 0 make the inequality true.
What type of inequality goes with |x|<7
it would be an "AND" ... since the values inside 7 and -7 make the inequality true.
|x + 6| = 2x
x = 6 ... x = 2 is extraneous since it does NOT work when you plug it back in
|-x| - |x| = what?
0 ... this is applying the property that |x| = |-x|
Solve:
-2 < 4 - 3a < 13
-3 < a < 2
solve:
|x| + 5 > 11
x > 6 or x < -6
True or False:
|x| <= |-x|
True ... they are equal so yes |x| is less than or equal to |-x|
5 * (1 + 3m) = 3 * (5m - 10)
No Solution ... since all the variables cancel out then the equation is false.
Solve & Graph:
5 > -2x + 7
1 < x ... open circle on 1 & shaded to the right
Solve & Graph:
-5 < 2 - h or 6h + 5 > 71
h < 7 or h > 11
Open circles on 7 & 11 shaded to the outside
Solve:
|x - 4| -3 < 5
-4 < x < 12
|1 - 4k| > -11
All Real Numbers ... since all absolute values are greater than any negative #
m ... rise over run ... rate of change ... the slope formula
| x + 6| = 3x
x = 3 ... x = (-6/4) is extraneous since it does not work when you plug it back in
Solve & Graph:
7v - 5 < 65 or -3v - 2 < -2
All Real Numbers ... since it is an "OR" graph that overlaps
Solve & Graph:
3 + 4*|3x + 7| > -89
All Real Numbers
Solve & Graph:
7 * |n / 3| - 9 < 12
-9 < n < 9
Open circles at -9 & 9 with the region between shaded
4 * |3x-4| + 10 = 6
NO SOLUTION ... since the Absolute Value equals a negative # once you isolate it
2 - 5*|5m - 5| = -73
x = 4 & x = -2
Solve & Graph:
A number 'b' is less than 0 and at least -8
-8 <= b < 0
Close circle on -8, open circle on 0, shaded in between
9*|r - 2| - 10 < -73
No Solution
Solve & Graph:
4*|6 - 2a| + 8 < 24
1 < a < 5
Open circles at 1 & 5 with the region between shaded