Expressions and Equations
Simplify -1-4(1+2)
What is "-13?"
-1-4(3)
-1-12
-13
If |x| = 4, values of x could include...
What are "-4 and 4?"
What is the special rule for solving inequalities that makes them different than just solving an equation?
What is "flip the sign when you multiply or divide by a negative?"
Describe what a typical "or" inequality looks like on a number line.
What is "two inequalities with rays pointing away from one another?"
What makes the "create two cases" step different for absolute value inequalities than regular inequalities?
What is "you must flip the inequality sign and the +/- sign?"
If C = 2pir , solve for r.
What is " C/(2pi) ?"
What are "x+2 = 3 and x+2 = -3?"
x > -3 in interval notation
What is "(-3, oo)?"
In the special case w > -1 or w >= 10, where would the inequality start on a number line?
What is "the number line would start at the -1 because it is an or inequality, so the solution includes every value that at least one of the inequalities makes true?"
What are the two cases for |7-a|>2?
What are "7-a > 2 and 7-a < -2?"
Simplify 10a - 5ab if a = 2 and b = 1
What is "10?"
10(2) - 5(2)(1)
20 - 10(1)
20 - 10
10
Solve for x. |-7-4x|=17
What are "-6, 2.5?"
-7 - 4x = 17 -7 - 4x = -17
-4x = 24 -4x = -10
x = -6 x = 2.5
Solve 33x - (3x + 9) > -9.
What is "x > 0?"
33x - 3x - 9 > -9
30x - 9 > -9
30x > 0
x > 0
Solve -18<=2b-8<-8 . Write your answer as a simplified compound inequality triple.
What is " -5<=b<0 ?"
Solve
(|v-3|)/-5>-1
What is "-2 < v < 8?"
Or v > -2 and v < 8
Or (-2,8)
|v-3| < 5
v - 3 < 5 v - 3 > -5
v < 8 v > -2
Solve for k.
29k = 4k - (24 - k)
What is "-1?"
29k = 4k - 24 + k
29k = 5k - 24
24k = -24
k = -1
What is an erroneous solution?
Answers may vary, but key points include
*Occurs when the | | = a negative
*Values that you get from solving, but do not produce true statements when plugged back in
Solve -92 - 8k >= 23-(7-4k) .
What is " k<=-9 ?"
Provide the interval notation solution for
9y - 2 < 34 and 3y - 2 > -29.
What is "(-9,4)?"
Solve -3 - 6|4x - 10| < -87
What is "x < -1 or x > 6?"
-6|4x - 10| < -84
|4x - 10| > 14
4x - 10 > 14 4x - 10 < -14
4x > 24 4x < -4
x > 6 x < -1