Find the student’s error in solving the following inequality. 31 < –5x + 6 25 < –5x –5 < x
1 answer:
Answer:
He subtracted -5 from both sides, not -6
Step-by-step explanation:
The inequality that we have to solve in this problem is
To solve the inequality, we proceed as follows:
1)
First, we isolate the term in x. To do that, we add -6 on both sides of the inequality, and we find:
So, this is now the new inequality.
2)
Then, we divide both sides of the equation by 5; we get:
3)
Finally, we change sign to the inequality, so we get:
So, the student's error is that he subtracted -5 from both sides, not -6.
You might be interested in
<h2>Evaluating Composite Functions</h2><h3>Answer:</h3>
We can write how will be defined but that's too much work and it's only useful when we are evaluating
with many inputs.
First let's solve for first. As you read through this answer, you'll get the idea of what I'm doing.
Given:
Solving for :
Now we can solve for , since
,
.
Given:
Solving for :
Now we are can solve for . By now you should get the idea why
.
Given:
Solving for :
Answer:
The functions are inverses; f(g(x)) = x ⇒ answer D
⇒ answer D
Step-by-step explanation:
* <em>Lets explain how to find the inverse of a function</em>
- Let f(x) = y
- Exchange x and y
- Solve to find the new y
- The new y =
* <em>Lets use these steps to solve the problems</em>
∵
∵ f(x) = y
∴
- Exchange x and y
∴
- Square the two sides
∴ x² = y - 3
- Add 3 to both sides
∴ x² + 3 = y
- Change y by
∴
∵ g(x) = x² + 3
∴
∴ <u><em>The functions are inverses to each other</em></u>
* <em>Now lets find f(g(x))</em>
- To find f(g(x)) substitute x in f(x) by g(x)
∵
∵ g(x) = x² + 3
∴
∴ <u><em>f(g(x)) = x</em></u>
∴ The functions are inverses; f(g(x)) = x
* <em>Lets find the inverse of h(x)</em>
∵ h(x) = 3x² - 1 where x ≥ 0
- Let h(x) = y
∴ y = 3x² - 1
- Exchange x and y
∴ x = 3y² - 1
- Add 1 to both sides
∴ x + 1 = 3y²
- Divide both sides by 3
∴
- Take √ for both sides
∴ ±
∵ x ≥ 0
∴ We will chose the positive value of the square root
∴
- replace y by
∴
The mass of sodium chloride required for 1. 8 × 10^3 people is 3. 6 × 10^5 grams. Option A is the correct answer.
<h3>How do you calculate the mass of sodium chloride required?</h3>Given that weigh of the person is 50 KG. The mass of the sodium chloride in one person is given below.
The mass of sodium chloride is calculated as given below.
Hence we can conclude that the mass of sodium chloride required for 1. 8 × 10^3 people is 3. 6 × 10^5 grams. Option A is the correct answer.
To know more about the mass, follow the link given below.