Absolute value inequalities
What are the solutions to the inequality |x| < 4 ?
-4 < x < 4 (x must be between these numbers)
y + 5 < -x
Slope is -1, y-intercept is -5
x < -3 or x > 2
Is (1,3) one solution to the linear inequality y > 2x + 1
No. The point is on the line, but needs to be greater or somewhere above it to be a solution. For example, (1, 4 would be a solution)
Which of these tv shows have I never watched before
a) the office
b) breaking bad
c) game of thrones
d) stranger things
c) game of thrones
What are the solutions to the inequality |x - 2| ≥ 5
x ≥ 7 or x ≤ -3
What are the solutions to the inequality x2 - 6x + 5 < 0
By factoring, you find that this equals 0 when x = 5 and x = 1. The inequality is true (less than 0) between these, so
1 < x < 5
Is x = -4 a solution to the inequality |x - 2| > 5
Yes, -4 - 2 = -6 and its absolute value is 6, which is greater than 5.
By the way, all solutions to this inequality would be x < -3 or x > 7
What is my natural hair color?
Brown (I don't dye my hair)
What are the solutions to the inequality |4x| > -2
All real numbers, the absolute value of anything is always positive
Sketch a graph of this system of linear inequalities
y < 3x - 1
y > -2x + 2
DASHED lines, first line crosses through (0, -1) and (1, 2). Second line crosses through (0, 2) and (1, 0). The right side of the graph should be shaded!
Not needed, but these lines intersect at (0.6, 0.8)
What are the solutions to the inequality x(x - 1)(x - 3) ≥ 0
0 ≤ x ≤ 1, and x ≥ 3
Would (-1, 3) be a solution to the inequality y ≥ x2 + x + 3
Yes, 3 ≥ (-1)2 + -1 + 3 = 1 + -1 + 3 = 3
What are the only three cities/towns of Harford County (the rest are technically unincorporated places, such as forest hill)
Bel air (town), Aberdeen (city), Havre de Grace (city)
What are the solutions to the inequality |3x + 6| < 9
-5 < x < 1 (x must be between these numbers)
Graph this system of linear inequalities:
5x + y ≥ 3
y - 4 ≥ -6x
SOLID lines. First line contains a y-intercept of (0, 3) and passes through (1, -2)
Second line contains a y-intercept of (0, 4) and also passes through (1, -2)
Right side of the graph is shaded
What are the solutions to the inequality
3x2 + 2x - 10 ≥ 0
Solve using quadratic formula to find that it equals 0 when x = 1.52 and x = -2.19
The inequality is true when x > 1.52 or x < -2.19
Would (5, 0) be a solution to the following system of linear inequalities
x + 10y > 4
y > 2x
No, the first equation works because 5 + 10(0) = 5 which is greater than 4, however for the second,
0 > 2(5) = 10 is not true
Which of these retail stores did I work at during part of my time in college?
a) Five below
b) Marshall's
c) Gamestop
d) Verizon
a) Five below
What are the solutions to the inequality |-2x - 4| ≤ 8
-6 ≤ x ≤ 2 (x must be equal to or between these numbers)
Graph the following system of linear inequalities:
3x + 2y < 6
-2x - y ≤ 4
First line is DASHED, has a y-intercept of (0, 3) and a slope of -1.5 or -3/2
Second line is SOLID, has a y-intercept of (0, -4) and a slope of -2
Shade the bottom right between the two lines
What are the solutions to the inequality (x + 1)2(x - 2)2 > 0
Quartic equation with a double root at -1 and a double root at 2.
Inequality is only not true at these two values. So, if
x < -1, -1 < x < 2, or x > 2, then it is true
Would the point (0, -2) be a solution to the following system of linear inequalities
y > -3x - 5
2x - 3y > 0
Yes, -2 > -3(0) - 5 = -5
AND
2(0) - 3(-2) = 6 > 0
Each of these artists had one song in my Spotify top 100 except...
a) Tame Impala
b) The Beatles
c) Pink Floyd
d) Led Zeppelin
d) Led Zeppelin