Question

Applying the definition of module and simplifications, fill in the gaps. |𝑥| − 2|𝑥 − 3| = { 𝑥 − 6, 𝑠𝑒 𝑥 < 0 _, 𝑠𝑒 0 ≤ 𝑥 < , 𝑠𝑒_______

likes

279 views

Answer to a math question Applying the definition of module and simplifications, fill in the gaps. |𝑥| − 2|𝑥 − 3| = { 𝑥 − 6, 𝑠𝑒 𝑥 < 0 _, 𝑠𝑒 0 ≤ 𝑥 < , 𝑠𝑒_______

$Expert avatar$

Rasheed

4.7

110 Answers

|x| - 2|x - 3| = \begin{cases} x - 6, & \text{if } x < 0 \\3x - 6, & \text{if } 0 \leq x < 3 \\-x + 6, & \text{if } x \geq 3 \end{cases}

1. For $x < 0$:

|x| = -x \quad \text{and} \quad |x - 3| = -x + 3

-x - 2(-x + 3) = x - 6

2. For $0 \leq x < 3$:

|x| = x \quad \text{and} \quad |x - 3| = -x + 3

x - 2(-x + 3) = 3x - 6

3. For $x \geq 3$:

|x| = x \quad \text{and} \quad |x - 3| = x - 3

x - 2(x - 3) = -x + 6

Frequently asked questions (FAQs)

Math question: How many pairs of corresponding sides and angles should be congruent in order to prove triangles congruent using the SAS (side-angle-side) rule?

Question: What is the derivative of f(x) = 5x^3 - 2x^2 + 7x + 2?

What is 0.75 expressed as a percent?

New questions in Mathematics

find the value of the tangent if it is known that the cos@= 1 2 and the sine is negative. must perform procedures.

-x+3x-2,si x=3

Karina has a plot of 5,000 square meters in which she has decided that 60% of it will be used to plant vegetables. Of this part, 12% will be dedicated to planting lettuce. How much surface area of the plot will be used for cultivation?

Given the vectors: a = (2m – 3n, 4n – m) and b = (2, -3), find the values of m and n that make: a = 5 b.

5) A family with a father, mother and 3 children must sit on five chairs in a row and the only restriction is that the mother must be at one end. In how many different ways can they be seated?

(3x^(2) 9x 6)/(5x^(2)-20)

Find the equation of the line perpendicular to −5𝑥−3𝑦+5=0 passing through the point (0,−2)

Is -11/8 greater than or less than -1.37?

(2m+3)(4m+3)=0

On+January+10+2023+the+CONSTRUCTORA+DEL+ORIENTE+SAC+company+acquires+land+to+develop+a+real estate+project%2C+which+prev%C3% A9+enable+50+lots+for+commercial+use+valued+in+S%2F+50%2C000.00+each+one%2C+the+company+has+as+a+business+model+generate+ cash+flow+through%C3%A9s+of+the+rental%2C+so+47%2C+of+the+50+enabled+lots+are+planned to lease+47%2C+and+ the+rest+will be%C3%A1n+used+by+the+company+for+management%C3%B3n+and+land+control

Let f and g be defined in R and suppose that there exists M > 0 such that |f(x) − f(p)| ≤ M|g(x) − g(p)|, for all x. Prove that if g is continuous in p, then f will also be continuous in p.

A diamond ring was reduced from $999.99 to $689.99. Find the percent reduction in the price. Round the answer to the nearest tenth of a percent, if necessary.

2x-5-x+2=5x-11

A post office has three categories of letters: 60% are from businesses, 30% are individual mail, and the remaining 10% are government mail. 5% of the letters from businesses have address errors, 10% of the individual mail has address errors, while 1% of the government mail has address errors. If we receive a letter with an address error, what is the probability that it is individual mail?"

To paint a 250 m wall, a number of workers were employed. If the wall were 30 m longer, 9 more workers would be needed. How many were employed at the beginning?

The perimeter of a rectangular rug is 42 feet. The width is 9 feet. What is the length?

-1/3x+15=18

Carmen's age was twice as old as Luis was when Carmen was Luis's age. When Luis is Carmen's age, their ages will add up to 112.

64-6x^2>0

Write an equation of the affine function whose graph is perpendicular to the graph of f(x) = 5x − 1 and passes through the point (5, 20).

Applying the definition of module and simplifications, fill in the gaps. |𝑥| − 2|𝑥 − 3| = { 𝑥 − 6, 𝑠𝑒 𝑥 < 0 ___________, 𝑠𝑒 0 ≤ 𝑥 < ______ ______, 𝑠𝑒_________________

Answer to a math question Applying the definition of module and simplifications, fill in the gaps. |𝑥| − 2|𝑥 − 3| = { 𝑥 − 6, 𝑠𝑒 𝑥 < 0 ___________, 𝑠𝑒 0 ≤ 𝑥 < ______ ______, 𝑠𝑒_________________

You might be interested in

Applying the definition of module and simplifications, fill in the gaps. |𝑥| − 2|𝑥 − 3| = { 𝑥 − 6, 𝑠𝑒 𝑥 < 0 _, 𝑠𝑒 0 ≤ 𝑥 < , 𝑠𝑒_______

Answer to a math question Applying the definition of module and simplifications, fill in the gaps. |𝑥| − 2|𝑥 − 3| = { 𝑥 − 6, 𝑠𝑒 𝑥 < 0 _, 𝑠𝑒 0 ≤ 𝑥 < , 𝑠𝑒_______