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kaheart [24]
3 years ago
15

Solve 3x + 5 ⩾ x + 17

Mathematics
1 answer:
Ugo [173]3 years ago
5 0

Answer:

Step-by-step explanation:

Simplifying

3x + 5 = x + 17

Reorder the terms:

5 + 3x = x + 17

Reorder the terms:

5 + 3x = 17 + x

Solving

5 + 3x = 17 + x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1x' to each side of the equation.

5 + 3x + -1x = 17 + x + -1x

Combine like terms: 3x + -1x = 2x

5 + 2x = 17 + x + -1x

Combine like terms: x + -1x = 0

5 + 2x = 17 + 0

5 + 2x = 17

Add '-5' to each side of the equation.

5 + -5 + 2x = 17 + -5

Combine like terms: 5 + -5 = 0

0 + 2x = 17 + -5

2x = 17 + -5

Combine like terms: 17 + -5 = 12

2x = 12

Divide each side by '2'.

x = 6

Simplifying

x = 6

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What are the domain and range of f(x) = 2(3X)?
erik [133]
<h3>Answer: Choice A</h3>

Domain: (-\infty,\infty)

Range: (0,\infty)

==============================================================

Explanation:

I'm assuming the function is f(x) = 2(3)^x which is an exponential function.

The domain of any exponential function is the set of real numbers. In interval notation, the domain is (-\infty, \infty) which says we can pick any number between negative infinity and positive infinity: aka any number we want. There are no restrictions to worry about such as division by zero errors.

The range of this exponential function is the set of y values such that y > 0. It often helps to see the graph of what is going on (see below). Note how as x heads to the left, and gets more negative, the curve approaches the x axis. It never actually touches it however. So it will never reach y = 0 itself but instead just get very close. The inequality y > 0 translates to the interval notation (0,\infty)

----------

Summary:

Domain: (-\infty,\infty);  Range: (0,\infty)

So that's why the answer is choice A

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Answer:

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4 years ago
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