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sergiy2304 [10]
3 years ago
11

|2x| ≤ x + 3

Mathematics
2 answers:
Korolek [52]3 years ago
5 0

Let's solve your inequality step-by-step.

|2x|≤x+3

Solve Absolute Value.

|2x|≤x+3

Let's find the critical points of the inequality.

|2x|=x+3

We know either2x=x+3or2x=−(x+3)

2x=x+3(Possibility 1)

2x−x=x+3−x(Subtract x from both sides)

x=3

2x=−(x+3)(Possibility 2)

2x=−x−3(Simplify both sides of the equation)

2x+x=−x−3+x(Add x to both sides)

3x=−3

3x

3

=

−3

3

(Divide both sides by 3)

x=−1

Check possible critical points.

x=3(Works in original equation)

x=−1(Works in original equation)

Critical points:

x=3 or x=−1

Check intervals in between critical points. (Test values in the intervals to see if they work.)

x≤−1(Doesn't work in original inequality)

−1≤x≤3(Works in original inequality)

x≥3(Doesn't work in original inequality)

Answer:

−1≤x≤3

r-ruslan [8.4K]3 years ago
3 0

Answer:

[-1,3]

Step-by-step explanation:

|2x|<x+3

calculate the absolute value

2*|x|<x+3

move < to left

2*|x|-x<3

split into possible cases

2x-x<3, x<0

2*(-x)-x<3, x<0

solve inequalities

[0,3]

[-1,0]

find union

[-1,3]

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Step-by-step explanation:

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Please help quick will give brainliest
Snowcat [4.5K]

25t means "25 times t" where t is some unknown number. It is a placeholder for a number.

To find what the number is, we undo what is happening to t. So we divide both sides by 25 to undo the operation "multiply by 25"

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25*t = 1125

25*t/25 = 1125/25 divide both sides by 25

t = 45

---------

<h3>Answer: 45</h3>

As a check, we can plug t = 45 into the equation and we should get the same value on both sides

25*t = 1125

25*45 = 1125 replace every t with 45

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V2 - 15 = -2v Solve the Quadratic. What are the 2 solutions?
ki77a [65]

Answer:

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Step-by-step explanation:

We are given that

v^2-15=-2v

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v(v+5)-3(v+5)=0

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Substitute each factor equal to 0

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