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3 years ago

Find m (-3x + 20) (-2x + 55)

Mathematics

1 answer:

Sergeeva-Olga [200]3 years ago

6 0

Answer: Solution for (-3x+20)+(-2x+55)=180 equation: x= -21

Step-by-step explanation:

Simplifying

(-3x + 20) + (-2x + 55) = 180

Reorder the terms:

(20 + -3x) + (-2x + 55) = 180

Remove parenthesis around (20 + -3x)

20 + -3x + (-2x + 55) = 180

Reorder the terms:

20 + -3x + (55 + -2x) = 180

Remove parenthesis around (55 + -2x)

20 + -3x + 55 + -2x = 180

Reorder the terms:

20 + 55 + -3x + -2x = 180

Combine like terms: 20 + 55 = 75

75 + -3x + -2x = 180

Combine like terms: -3x + -2x = -5x

75 + -5x = 180

Solving

75 + -5x = 180

Solving for variable 'x'.

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

Add '-75' to each side of the equation.

75 + -75 + -5x = 180 + -75

Combine like terms: 75 + -75 = 0

0 + -5x = 180 + -75

-5x = 180 + -75

Combine like terms: 180 + -75 = 105

-5x = 105

Divide each side by '-5'.

x = -21

Simplifying

x = -21

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$\begin{bmatrix}3x+5y=10\\ 2x+ay=4\end{bmatrix}$

$\mathrm{Multiply\:}3x+5y=10\mathrm{\:by\:}2: 6x+10y=20$
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$\begin{bmatrix}6x+10y=20\\ 3a-10y=-8\end{bmatrix}$

$3a-10y=-8 \ \textgreater \ \mathrm{Subtract\:}3a\mathrm{\:from\:both\:sides}$
$3a-10y-3a=-8-3a$

$\mathrm{Simplify} \ \textgreater \ -10y=-8-3a \ \textgreater \ \mathrm{Divide\:both\:sides\:by\:}-10$
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$\frac{-10y}{-10} \ \textgreater \ \mathrm{Apply\:the\:fraction\:rule}: \frac{-a}{-b}=\frac{a}{b} \ \textgreater \ \frac{10y}{10}$

$\mathrm{Divide\:the\:numbers:}\:\frac{10}{10}=1 \ \textgreater \ y$

$-\frac{8}{-10}-\frac{3a}{-10} \ \textgreater \ \mathrm{Apply\:rule}\:\frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c} \ \textgreater \ \frac{-8-3a}{-10}$

$\mathrm{Apply\:the\:fraction\:rule}: \frac{a}{-b}=-\frac{a}{b} \ \textgreater \ -\frac{-3a-8}{10} \ \textgreater \ y=-\frac{-8-3a}{10}$

$\mathrm{For\:}6x+10y=20\mathrm{\:plug\:in\:}\ \:y=\frac{8}{10-3a} \ \textgreater \ 6x+10\cdot \frac{8}{10-3a}=20$

$10\cdot \frac{8}{10-3a} \ \textgreater \ \mathrm{Multiply\:fractions}: \:a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c} \ \textgreater \ \frac{8\cdot \:10}{10-3a}$
$\mathrm{Multiply\:the\:numbers:}\:8\cdot \:10=80 \ \textgreater \ \frac{80}{10-3a}$

$6x+\frac{80}{10-3a}=20 \ \textgreater \ \mathrm{Subtract\:}\frac{80}{10-3a}\mathrm{\:from\:both\:sides}$
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