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2 years ago

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If the first step in the solution of the equation 2x - 8 = 5x + 3 is "subtract 2x," then in the form of a paragraph, explain in

complete sentences the next steps necessary to completely solve the equation for x. Include the final answer in your explanation.

1 answer:

monitta2 years ago

3 0

$x = \frac{-11}{3}$

<u>Step-by-step explanation:</u>

Here we have , If the first step in the solution of the equation 2x - 8 = 5x + 3 is "subtract 2x," then in the form of a paragraph, explain in complete sentences the next steps necessary to completely solve the equation for x. Let's solve this :

2x - 8 = 5x + 3

⇒ $2x - 8 = 5x + 3$

⇒ $(2x - 8)-2x = (5x + 3)-2x$ { subtract 2x from both side }

⇒ $0 - 8 = 5x-2x + 3$

⇒ $- 8 = 3x + 3$

⇒ $- 8 -3= 3x + 3-3$ { subtract 3 from both sides }

⇒ $- 11 = 3x + 0$

⇒ $- 11 = 3x$

⇒ $\frac{-11}{3} = \frac{3}{3} x$ { divide 3 from both sides }

⇒ $x = \frac{-11}{3}$

You might be interested in

Dy/dx = 2xy^2 and y(-1) = 2 find y(2)

Anarel [89]

If you're using the app, try seeing this answer through your browser: brainly.com/question/2887301

—————

Solve the initial value problem:

dy
——— = 2xy², y = 2, when x = – 1.
dx

Separate the variables in the equation above:

$\mathsf{\dfrac{dy}{y^2}=2x\,dx}\\\\
\mathsf{y^{-2}\,dy=2x\,dx}$

Integrate both sides:

$\mathsf{\displaystyle\int\!y^{-2}\,dy=\int\!2x\,dx}\\\\\\
\mathsf{\dfrac{y^{-2+1}}{-2+1}=2\cdot \dfrac{x^{1+1}}{1+1}+C_1}\\\\\\
\mathsf{\dfrac{y^{-1}}{-1}=\diagup\hspace{-7}2\cdot \dfrac{x^2}{\diagup\hspace{-7}2}+C_1}\\\\\\
\mathsf{-\,\dfrac{1}{y}=x^2+C_1}$

$\mathsf{\dfrac{1}{y}=-(x^2+C_1)}$

Take the reciprocal of both sides, and then you have

$\mathsf{y=-\,\dfrac{1}{x^2+C_1}\qquad\qquad where~C_1~is~a~constant\qquad (i)}$

In order to find the value of C₁ , just plug in the equation above those known values for x and y, then solve it for C₁:

y = 2, when x = – 1. So,

$\mathsf{2=-\,\dfrac{1}{1^2+C_1}}\\\\\\
\mathsf{2=-\,\dfrac{1}{1+C_1}}\\\\\\
\mathsf{-\,\dfrac{1}{2}=1+C_1}\\\\\\
\mathsf{-\,\dfrac{1}{2}-1=C_1}\\\\\\
\mathsf{-\,\dfrac{1}{2}-\dfrac{2}{2}=C_1}$

$\mathsf{C_1=-\,\dfrac{3}{2}}$

Substitute that for C₁ into (i), and you have

$\mathsf{y=-\,\dfrac{1}{x^2-\frac{3}{2}}}\\\\\\
\mathsf{y=-\,\dfrac{1}{x^2-\frac{3}{2}}\cdot \dfrac{2}{2}}\\\\\\
\mathsf{y=-\,\dfrac{2}{2x^2-3}}$

So y(– 2) is

$\mathsf{y\big|_{x=-2}=-\,\dfrac{2}{2\cdot (-2)^2-3}}\\\\\\
\mathsf{y\big|_{x=-2}=-\,\dfrac{2}{2\cdot 4-3}}\\\\\\
\mathsf{y\big|_{x=-2}=-\,\dfrac{2}{8-3}}\\\\\\
\mathsf{y\big|_{x=-2}=-\,\dfrac{2}{5}}\quad\longleftarrow\quad\textsf{this is the answer.}$

I hope this helps. =)

Tags: <em>ordinary differential equation ode integration separable variables initial value problem differential integral calculus</em>

7 0

3 years ago

Please answer quick! Thank You! Math

Musya8 [376]

I believe it is B.) Alternate Interior.

4 0

2 years ago

Read 2 more answers

vredina [299]

The answer to you question is B for number 1 and for 2 it is C. Hope this helps

4 0

3 years ago

Read 2 more answers

Math question down below

Vilka [71]

The answer is c, 30/7

6 0

3 years ago

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Suppose a large shipment of telephones contained 21% defectives. If a sample of size 498 is selected, what is the probability th

grandymaker [24]

Answer:

$P(-3\% < x < 3\%) = 0.901$

Step-by-step explanation:

Given

$p = 21\%$

$n = 498$

Required

$P(-3\% < x < 3\%)$

First, we calculate the z score

$z = \sqrt{p * (1 - p)/n}$

$z = \sqrt{21\% * (1 - 21\%)/498}$

$z = \sqrt{21\% * (79\%)/498}$

$z = \sqrt{0.1659/498}$

$z = \sqrt{0.000333}$

$z = 0.0182$

So:

$P(-3\% < x < 3\%) = P(-3\%/0.0182 < z$

$P(-3\% < x < 3\%) = P(1.648 < z$

From z probability, we have:

$P(-3\% < x < 3\%) = 0.901$

6 0

2 years ago