Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve for zz.\newline−∣z∣≤−4-|z| \leq -4\newline\newlineWrite a compound inequality like 1 < x < 3 or like x < 1 or x > 3. Use integers, proper fractions, or improper fractions in simplest form.\newline______

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Solve absolute value inequalitiesright chevron icon

Full solution

Q. Solve for zz.\newline−∣z∣≤−4-|z| \leq -4\newline\newlineWrite a compound inequality like 1<x<31 < x < 3 or like x<1x < 1 or x>3x > 3. Use integers, proper fractions, or improper fractions in simplest form.\newline______
  1. Isolate absolute value term: We have the inequality: \newline−∣z∣≤−4-|z| \leq -4\newlineFirst, we need to isolate the absolute value term ∣z∣|z|. To do this, we can multiply both sides of the inequality by −1-1, remembering that this reverses the inequality sign.\newline−1⋅(−∣z∣)≥−1⋅(−4)-1 \cdot (-|z|) \geq -1 \cdot (-4)\newline∣z∣≥4|z| \geq 4
  2. Interpret compound inequality: Now that we have ∣z∣≥4|z| \geq 4, we can interpret this as zz being either greater than or equal to 44 or less than or equal to −4-4. This is because the absolute value of zz is the distance from 00 on the number line, and it can be either positive or negative.\newlineSo, the compound inequality is:\newlinez≥4z \geq 4 or z≤−4z \leq -4

More problems from Solve absolute value inequalities

Question
Solve for ss.\newline∣s∣+3≥8|s| + 3 \geq 8
Get tutor helpright-arrow

Posted 4 months ago

Question
Which compound inequality represents the value of x?x ? \newline(x−1)(x+1)>0(x - 1)(x + 1) > 0\newline
Get tutor helpright-arrow

Posted 4 months ago

Question
A particular company charges advertisers a one time cost of $500\$500, in addition to $4.50\$4.50 for every one thousand times an advertisement is shown on the company's webpage. An advertiser wants its ad to appear MM thousand times on the webpage, but does not want to spend more than $5,000\$5,000. Which of the following inequalities best describes the situation? \newlineChoices: \newline(A) 500+4.50M≥5,000500+4.50M\geq5,000 \newline(B) 4.50+500M>5,0004.50+500M>5,000 \newline(C) 500+4.50M≤5,000500+4.50M\leq5,000 \newline(D) 500+4.50M<5,000500+4.50M<5,000
Get tutor helpright-arrow

Posted 7 months ago

Question
7x+1<x+97x+1 < x+9\newlineWhich of the following best describes the solutions to the inequality shown?\newlineChoose 11 answer:\newline(A) x>43x > \frac{4}{3}\newline(B) x<43x < \frac{4}{3}\newline(C) x<1x < 1\newline(D) x<53x < \frac{5}{3}
Get tutor helpright-arrow

Posted 4 months ago

Question
52−3x<−1452-3x < -14\newlineWhich of the following best describes the solutions to the inequality shown?\newlineChoose 11 answer:\newline(A) x>−383x > -\frac{38}{3}\newline(B) x>383x > \frac{38}{3}\newline(C) x<22x < 22\newline(D) x>22x > 22
Get tutor helpright-arrow

Posted 10 months ago

Question
5−3x>2x+25-3x > 2x+2\newlineWhich of the following best describes the solutions to the inequality shown?\newlineChoose 11 answer:\newline(A) x<75x < \frac{7}{5}\newline(B) x<3x < 3\newline(C) x<35x < \frac{3}{5}\newline(D) x>35x > \frac{3}{5}
Get tutor helpright-arrow

Posted 10 months ago

Question
Rani is a real estate agent. For each house she sells, she pays $100 \$ 100 in fees, but earns a commission of 1.8% 1.8 \% of the selling price of the house. Rani's total profit from a particular house is $4,580 \$ 4,580 . If p p represents the selling price of the house, which equation best models the situation?\newlineChoose 11 answer:\newline(A) 0.018p−100=4580 0.018 p-100=4580 \newline(B) 0.018p+100=4580 0.018 p+100=4580 \newline(C) (100−0.018)p=4580 (100-0.018) p=4580 \newline(D) (100+0.018)p=4580 (100+0.018) p=4580
Get tutor helpright-arrow

Posted 8 months ago

Question
A commercial airplane that is 11,500500 miles into a 22,500500 -mile journey is traveling at 450450 knots in still air when it picks up a tailwind of 150150 knots (in the same direction). If h h is the number of hours remaining in the airplane's flight, which of the following equations best describes the situation?\newline11 knot=1.15\mathrm{knot}=1.15 miles per hour (mph)\newlineChoose 11 answer:\newline(A) 1,500+690h=2,500 1,500+690 h=2,500 \newline(B) 1,500+600h=2,500 1,500+600 h=2,500 \newline(C) 1,500−600h=2,500 1,500-600 h=2,500 \newline(D) 1,500−690h=2,500 1,500-690 h=2,500
Get tutor helpright-arrow

Posted 7 months ago

Question
A weeping willow that is 1515 feet in height grows to a maximum height of 3535 feet in y y years at a constant rate of 2424 inches per year. Which of the following equations best describes this situation?\newline11 foot =12 =12 inches\newlineChoose 11 answer:\newline(A) 35=15+2y 35=15+2 y \newline(B) 35=15+24y 35=15+24 y \newline(C) 35=15−2y 35=15-2 y \newline(D) 35=15−24y 35=15-24 y
Get tutor helpright-arrow

Posted 10 months ago

Question
The gas mileage for a car is 2323 miles per gallon when the car travels at 6060 miles per hour. The car begins a trip with 1313 gallons in its tank, travels at an average speed of 6060 miles per hour for h h hours, and ends the trip with 1010 gallons in its tank. Which of the following equations best models this situation?\newlineChoose 11 answer:\newline(A) 13−23h60=10 13-\frac{23 h}{60}=10 \newline(B) 13−60h23=10 13-\frac{60 h}{23}=10 \newline(C) 13−60h23=10 \frac{13-60 h}{23}=10 \newline(D) 13−23h60=10 \frac{13-23 h}{60}=10
Get tutor helpright-arrow

Posted 8 months ago

View all (74)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant