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3 years ago

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3x − 15= 3x + 15 what is x?

1 answer:

Marina CMI [18]3 years ago

7 0

We are given the following equation and want to find the possible values of x

$3x-15=3x+15$

Subtract both sides by 3x

$3x-15-3x=3x+15-3x$

$-15=15$

Now, we have this weird equation. Since -15 is NOT equal 15 and there is no other way we could have solved for x, there is no real solution to the given equation.

In other words, there is no value of x that makes the equation true.

Let me know if you need any clarifications, thanks!

~ Padoru

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A) What is the equation of the line that passes through the given pair points in slope-intercept form?

lesya [120]

A)

The slope-intercept form:

$y=mx+b$

m - slope

b - y-intercept

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

We have the points (2, 5.1) and (-1, -0.5). Substitute:

$m=\dfrac{-0.5-5.1}{-1-2}=\dfrac{-5.6}{-3}=\dfrac{5.6}{3}=\dfrac{56}{30}=\dfrac{28}{15}$

Therefore we have:

$y=\dfrac{28}{15}x+b$

Put the coordinates of the point (-1, -0.5) ot the equation:

$-0.5=\dfrac{28}{15}(-1)+b$

$-0.5=-\dfrac{28}{15}+b$ <em>multiply both sides by 2</em>

$-1=-\dfrac{56}{15}+2b$ <em>add $\dfrac{56}{15}$ to both sides</em>

$\dfrac{41}{15}=2b$ <em>divide both sides by 2</em>

$b=\dfrac{41}{30}$

Answer: $\boxed{y=\dfrac{28}{15}x+\dfrac{41}{30}}$

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B)

We have the points (-2, 3) and (3, -4).

Calculate the slope:

$m=\dfrac{-4-3}{3-(-2)}=\dfrac{-7}{5}=-\dfrac{7}{5}$

Therefore we have:

$y=-\dfrac{7}{5}x+b$

Put the coordinates of the point (-2, 3) to the equation of a line:

$3=-\dfrac{7}{5}(-2)+b$

$\dfrac{15}{5}=\dfrac{14}{5}+b$ <em>subtract $\dfrac{14}{5}$ from both sides</em>

$\dfrac{1}{5}=b\to b=\dfrac{1}{5}$

Answer: $\boxed{y=-\dfrac{7}{5}x+\dfrac{1}{5}}$

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3 years ago