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3 years ago

5x-3 =2x+15 Someone pls help for geometry

Mathematics

1 answer:

inysia [295]3 years ago

5 0

Answer:

x = 6

Step-by-step explanation:

5x-3 = 2x+15

<h3>i) move 2x to the left-hand side and change its sign</h3>

5x-2x-3 = 15

<h3>ii) move -3 to the right-hand side and change its sign</h3>

5x-2x = 15+3

<h3>iii) collect like terms</h3>

3x = 15+3

<h3>iv) add the numbers</h3>

3x = 18

<h3>v) divide both sides of the equation by 3</h3>

$\frac{3x}{3} = \frac{18}{ 3}$

$x = 6$

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a) Since both limits are <em>distinct</em> and do not exist, we conclude that x = - 1 is not part of the domain of the <em>rational</em> function.

b) The function $f(x) = \frac{x}{x^{2}+ x}$ is equivalent to the function $g(x) = \frac{1}{x + 1}$ .

<h3>How to determine whether a limit exists or not</h3>

According to theory of limits, a function f(x) exists for x = a if and only if $\lim_{x\to a^{-}} f(x) = \lim_{x \to a^{+}} f(x)$ . This criterion is commonly used to prove continuity of functions.

<em>Rational</em> functions are not continuous for all value of x, as there are x-values that make denominator equal to 0. Based on the figure given below, we have the following <em>lateral</em> limits:

$\lim_{x \to -1^{-}} \frac{x}{x^{2}+x} = - \infty$

$\lim_{x \to -1^{+}} \frac{x}{x^{2}+x} = + \infty$

Since both limits are <em>distinct</em> and do not exist, we conclude that x = - 1 is not part of the domain of the <em>rational</em> function.

In addition, we can simplify the function by <em>algebra</em> properties:

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$g(x) = \frac{1}{x + 1}$

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To learn more on lateral limits: brainly.com/question/21783151

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