Algebra 2- Absolute Value and Compound Inequalities

When an abs value equation equals 0 how many solutions will there be

1

∣x∣=x infinitely many solutions or no solution

Infinitely Many Solutions ( we are talking about numbers that are 0 or greater, idk why that's what Garcia said though)

Determine numbers in the set are integers, rational numbers, and irrational numbers: -6, 5

Integers

when you see the word and in a compound equation what does it mean

Intersection

Determine numbers in the set are integers, rational numbers, and irrational numbers: -6, 0.7, 5, -1/3,

Rational numbers

Write an absolute value equation that has the given solution(s): 5

∣x-5∣=0

Maria'a parents live 10 miles down the same road as her and her young children. If her parents agree to watch her children while she works, where along the road could Margo( I think that should be Maria?) find a job so that she can take her children to her parents, go to work, pick them up and return home while only driving a total of 25 miles? Write an abs value equation to model the following.

12.5 and 7.5 ∣x-10∣=2.5

When an abs value equation equals a positive number how many solutions will there be

2

The average number of seeds in a package of cucumber seeds is 25. The number of seeds in the package can vary by three. What are the maximum and minimum number of seeds that could be in a package? Write an absolute value equation to model each of the following

22 and 28 ∣x-25∣=3

A submarine begins its descent from sea level to 300 feet below sea level. If the submarine travels x feet to avoid an obstacle and then returns to its 300 feet, what possible depths could the submarine have gone if the total vertical distance traveled was 524 feet. Write and abs value equation to model each of the following

412 and 188 ∣x-300∣=112

Members of the track team can run 400 m in an average time of 60 s. The fastest and slowest times varied from the average by 6.5 s. What were the maximum and minimum for the track time.

66.5 and 53.5 ∣x-60∣=6.5

What is an extraneous solution

Values (solutions) that do not make the original equation true

Solve the equation ∣2x + 3∣ = x-5. Which one of the following would be the solution(s)? a. no solution b. {-8} c. {2/3} d. {2/3, -8} e. none of these

a

Solve the equation -1/2∣6x-5∣ = 2x-3. Which one of them following statements describes the solution(s) for the equation? a. the solution for this equation are two positive rational numbers b. the solutions for this equation are one one positive and one negative rational number. c. The solutions for this equation are two negative rational number d. There is only one rational solution for this equation e . none of these

b

Solve the equation ∣3x+2∣=7. Which of the following would be the solution(s)? a. {7/3, -2} b. {3, -7/3} c. {1/3, 2} d. {5/3, -3} e. none of these

d

Solve the equation ∣4x-7∣= 17 I. -6 II. 5/2 III. 6 IV. -5/2 V. No solution a. I only b. II only c. I and II d. III and IV e. V only

d

Solve the equation ∣8-x∣=12. If there is only one solution, say so: otherwise find the product of the solutions a. There is only solution x= -4 b. There is only solution x=20 c. The product of the solutions is -40 d. The product of the solutions is 80 e. None of these

e

Solve the equation: -5∣2x-1∣+3=-10. Which of the following would be the solution(s)? a.{9/5} b. {9/5, -1/5} c. { 9/5, 4/5} d. no solution e. None of these

e

What are the extraneous solutions to the equations ∣3x+2∣=∣x+26∣ +2. Show all work(obvi not here but yk what I mean lol)

{11}

Determine numbers in the set are integers, rational numbers, and irrational numbers: √3 and pi

irrational numbers

5∣6-5x∣=15x-35 infinitely many solutions or no solution

no solution

When an abs value equation equals a negative number how many solutions will there be

no solution

-∣4-8b∣=12 infinitely many solutions or no solution

no solution ( value of equation cant be -)

∣x∣=-x Always, sometimes, or never

sometimes( x can be 0!)

What does this mean in a compound equation: U

union,or

∣2x-5∣= 4x-3

x=4/3

∣ax+bx∣=cd solve for x and list restrictions

x=cd/a+b, a=/ -b, x= -cd/a+b

Solve the equation ay+c=y-bc for y. Show all work

y= -bc-c/a-1 a=/1

GO READ THE DESCRIPTION IF YOU HAVENT ALRDY! ( the answer for this is just the word yes)

yes

What are the real solutions for this: ∣3x+2∣=∣x+26∣ +2.

{-15/2, 13}

Write an absolute value equation that has the given solution(s): -10 & 2

∣x+4∣= 6