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2 years ago

The value of x for which 3 (x-2) = 2 (x+1)

Mathematics

1 answer:

netineya [11]2 years ago

7 0

Answer:

x = 8

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Step-by-step explanation:

Step 1: Define equation

3(x - 2) = 2(x + 1)

Step 2: Solve for x

Distribute: 3x - 6 = 2x + 2
Subtract 2x on both sides: x - 6 = 2
Add 6 to both sides: x = 8

Step 3: Check

Plug in x into the original equation to verify it's a solution.

Substitute in x: 3(8 - 2) = 2(8 + 1)
Subtract/Add: 3(6) = 2(9)
Multiply: 18 = 18

Here we see that 18 does indeed equal 18.

∴ x = 8 is a solution to the equation.

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A restaurant served 27,500 customers in 2012. In 2014, the restaurant served 29,000 customers. Write a linear model that represe

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Answer:

In 2012, a restaurant served 27,500 customers and in 2014, the restaurant served 29,000 customers.

First determine the increase in the number of customer served each year.

the number of customer increase in each year is, $\frac{29000-27500}{2} =\frac{1500}{2} =750$

therefore, the linear model is;

y = 750x+ 27500 , where y represents the number of customers that the restaurant serves x years after 2012.

Now, to predict the number of customers that the restaurant will serve in 2020 is;

since, x = 2020-2012 = 8 years

$y = 750 \times 8 +27500$ or

$y= 6000+27500=33,500$

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2 years ago

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Answer:

The line equation in slope-intercept form is:

$y\:=-\frac{2}{5}x+4$

Hence, option D is true.

Step-by-step explanation:

Given the points

(0, 4)

(5, 2)

Finding the slope between the points

$\left(x_1,\:y_1\right)=\left(0,\:4\right),\:\left(x_2,\:y_2\right)=\left(5,\:2\right)$

$\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{2-4}{5-0}$

$m=-\frac{2}{5}$

As the y-intercept is obtained by setting the value x = 0.

As we know that when x = 0, the vale of y-intercept y = 4

so the y-intercept is b = 4.

As the slope-intercept form is

substituting the slope m = -2/5 and the y-intercept b=4

$y = mx+b$

$y\:=-\frac{2}{5}x+4$

Therefore, the line equation in slope-intercept form is:

$y\:=-\frac{2}{5}x+4$

Hence, option D is true.

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2 years ago

The value of x for which 3 (x-2) = 2 (x+1)​

The value of x for which 3 (x-2) = 2 (x+1)