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3 years ago

Solve for x. 6x - 3 = 21 - 2x (SHOW YOUR WORK)

Mathematics

2 answers:

patriot [66]3 years ago

5 0

Answer:

Simplifying

6x + -3 = 21 + -2x

Reorder the terms:

-3 + 6x = 21 + -2x

Solving

-3 + 6x = 21 + -2x

Solving for variable 'x'.

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

Add '2x' to each side of the equation.

-3 + 6x + 2x = 21 + -2x + 2x

Combine like terms: 6x + 2x = 8x

-3 + 8x = 21 + -2x + 2x

Combine like terms: -2x + 2x = 0

-3 + 8x = 21 + 0

-3 + 8x = 21

Add '3' to each side of the equation.

-3 + 3 + 8x = 21 + 3

Combine like terms: -3 + 3 = 0

0 + 8x = 21 + 3

8x = 21 + 3

Combine like terms: 21 + 3 = 24

8x = 24

Divide each side by '8'.

x = 3

Simplifying

x = 3

Step-by-step explanation:

rewona [7]3 years ago

3 0

Answer:x=3

Step-by-step explanation:first add 2x to both sides to get all the x's together

6x - 3 + 2x = 21

then add three to both sides to get the x's alone

6x + 2x = 21 + 3

simplify both sides of the equation

8x = 24

divide both sides by 8 to get x by itself

24/8 = 3

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vfiekz [6]

Answer:

$\displaystyle y=-0.927x+13.63$

Step-by-step explanation:

<u>Simple Linear Regression </u>

It a function that represents the relationship between two or more variables in a given data set. It uses the method of the least-squares regression line which minimizes the error between the estimate function and the real data.

Let's compute the best-fit line for the data

$x=\{1,5,6,12,15\}$

$y=\{14,11,4,2,1\}$

First, we find the sums

$\displaystyle \sum x=1+5+6+12+15=39$

$\displaystyle \sum y=14+11+4+2+1=32$

Then, we compute the averages values

$\displaystyle \bar{x}=\frac{39}{5}=7.8$

$\displaystyle \bar{y}=\frac{32}{5}=6.4$

We will also compute the sums of the cross-products and the sum of the squares

$\displaystyle \sum xy=(1)(14)+(5)(11)+(6)(4)+(12)(2)+(15)(1)=137$

$\displaystyle \sum x^2=1^2+5^2+6^2+12^2+15^2=1+25+36+144+225$

$\displaystyle \sum x^2=431$

We will compute Sxy and Sxx

$\displaystyle S_{xy}=\sum xy-\frac{\sum x\ \sum y}{n}$

$\displaystyle S_{xy}=137-\frac{(39)(32)}{5}$

$\displaystyle S_{xy}=-117.6$

$\displaystyle S_{xx}=\sum x^2-\frac{(\sum x)^2}{n}$

$\displaystyle S_{xx}=431-\frac{39}{5}^2=126.8$

The slope of the linear regression function is given by

$\displaystyle m=\frac{S_{xy}}{S_{xx}}=\frac{-117.6}{126.8}=-0.927$

The y-intercept ot the linear function is

$\displaystyle b=\bar{y}-b\bar{x}=6.4-(-0.927)(7.8)$

$\displaystyle b=13.63$

Thus the best-fit line is

$\displaystyle y=-0.927x+13.63$

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