How do you solve # |4k-2| =11#?

Answer 1

See a solution process below:

We must solve the term within the absolute value function for both its negative and positive equivalent because the absolute value function takes any term, whether positive or negative, and converts it to its positive form.

First Solution

#4k - 2 = -11#
#4k - 2 + color(red)(2) = -11 + color(red)(2)#
#4k - 0 = -9#
#4k = -9#
#(4k)/color(red)(4) = -9/color(red)(4)#
#(color(red)(cancel(color(black)(4)))k)/cancel(color(red)(4)) = -9/4#
#k = -9/4#

Option 2)

#4k - 2 = 11#
#4k - 2 + color(red)(2) = 11 + color(red)(2)#
#4k - 0 = 13#
#4k = 13#
#(4k)/color(red)(4) = 13/color(red)(4)#
#(color(red)(cancel(color(black)(4)))k)/cancel(color(red)(4)) = 13/4#
#k = 13/4#
The solutions are: #k = -9/4# and #k = 13/4#
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

#k in {-9/4, 13/4}#

The absolute value of #4k-2# must be 11, so #4k-2# must either be #+11# or #-11#.

You must divide this into two equations and solve each one in order to solve it.

Formula 1

#4k-2=11 color(white)"XXX."color(white)(1/x)# "4k-2" could be positive 11. #color(white)"XX-"4k = 13color(white)"XXXXX"# Add 2 to both sides. #color(white)"XXX"k=13/4color(white)"XXXX/"# Divide both sides by 4.

Formula 2

#4k-2=-11color(white)"X."color(white)(1/x)# "4k-2" could be negative 11. #color(white)"XX-"4k=-9 color(white)"XXXX"#Add 2 to both sides. #color(white)"XXX"k=-9/4color(white)"XXX"# Divide both sides by 4.
Therefore, our two solutions are #k = -9/4# and #k=13/4#.

We can more formally express our solution as follows since, in theory, we have a "set" of solutions:

#k in {-9/4, 13/4}#
(This means that #k# can be any element in the set containing #-9/4# and #13/4#)

Last Response

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 3

To solve (|4k - 2| = 11), consider both cases where the expression inside the absolute value can be positive or negative:

Case 1: (4k - 2 = 11)

(4k = 11 + 2)

(4k = 13)

(k = \frac{13}{4})

Case 2: (4k - 2 = -11)

(4k = -11 + 2)

(4k = -9)

(k = \frac{-9}{4})

Thus, (k = \frac{13}{4}) or (k = \frac{-9}{4}).

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7