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3 years ago

How many solutions does 17.75x + 24 = 18.95x + 18 have?

Mathematics

1 answer:

iren2701 [21]3 years ago

3 0

Answer: Simplifying

17.75x + 24 = 18.95x + 18

Reorder the terms:

24 + 17.75x = 18.95x + 18

Reorder the terms:

24 + 17.75x = 18 + 18.95x

Solving

24 + 17.75x = 18 + 18.95x

Solving for variable 'x'.

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

Add '-18.95x' to each side of the equation.

24 + 17.75x + -18.95x = 18 + 18.95x + -18.95x

Combine like terms: 17.75x + -18.95x = -1.2x

24 + -1.2x = 18 + 18.95x + -18.95x

Combine like terms: 18.95x + -18.95x = 0.00

24 + -1.2x = 18 + 0.00

24 + -1.2x = 18

Add '-24' to each side of the equation.

24 + -24 + -1.2x = 18 + -24

Combine like terms: 24 + -24 = 0

0 + -1.2x = 18 + -24

-1.2x = 18 + -24

Combine like terms: 18 + -24 = -6

-1.2x = -6

Divide each side by '-1.2'.

x = 5

Simplifying

x = 5

Step-by-step explanation:

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Solve the equation using the substitution u = y/x. When u = y/x is substituted into the equation, the equation becomes separable

bekas [8.4K]

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$\frac{u^2+3}{-u^3+u^2-2u}u'=\frac{1}{x}$

Step-by-step explanation:

First step: I'm going to solve our substitution for y:

$u=\frac{y}{x}$

Multiply both sides by x:

$ux=y$

Second step: Differentiate the substitution:

$u'x+u=y'$

Third step: Plug in first and second step into the given equation dy/dx=f(x,y):

$u'x+u=\frac{x(ux)+(ux)^2}{3x^2+(ux)^2}$

$u'x+u=\frac{ux^2+u^2x^2}{3x^2+u^2x^2}$

We are going to simplify what we can.

Every term in the fraction on the right hand side of equation contains a factor of $x^2$ so I'm going to divide top and bottom by $x^2$ :

$u'x+u=\frac{u+u^2}{3+u^2}$

Now I have no idea what your left hand side is suppose to look like but I'm going to keep going here:

Subtract u on both sides:

$u'x=\frac{u+u^2}{3+u^2}-u$

Find a common denominator: Multiply second term on right hand side by $\frac{3+u^2}{3+u^2}$ :

$u'x=\frac{u+u^2}{3+u^2}-\frac{u(3+u^2)}{3+u^2}$

Combine fractions while also distributing u to terms in ( ):

$u'x=\frac{u+u^2-3u-u^3}{3+u^2}$

$u'x=\frac{-u^3+u^2-2u}{3+u^2}$

Third step: I'm going to separate the variables:

Multiply both sides by the reciprocal of the right hand side fraction.

$u' \frac{3+u^2}{-u^3+u^2-2u}x=1$

Divide both sides by x:

$\frac{3+u^2}{-u^3+u^2-2u}u'=\frac{1}{x}$

Reorder the top a little of left hand side using the commutative property for addition:

$\frac{u^2+3}{-u^3+u^2-2u}u'=\frac{1}{x}$

The expression on left hand side almost matches your expression but not quite so something seems a little off.

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