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3 years ago

B. 2(3x - 5) = 2x + 6

Mathematics

2 answers:

Leto [7]3 years ago

8 0

Answer:

x = 4

Step-by-step explanation:

Given

2(3x - 5) = 2x + 6 ( divide both sides by 2 )

3x - 5 = x + 3 ( subtract x from both sides )

2x - 5 = 3 ( add 5 to both sides )

2x = 8 ( divide both sides by 2 )

x = 4

gogolik [260]3 years ago

6 0

Answer:

x = 4

Step-by-step explanation:

2(3x - 5) = 2x + 6

expand- 2(3x-5):6x+10

6x-10= 2x+6

Add 10 to both sides

6x-10+10=2x+6+10

simplify

6x=2x+16

subtract 2x from both sides

6x-2x=2x+16-2x

simplify

4x=16

divide both sides by 4

4x/4=16/4

x=4

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On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, negative 2) an

ExtremeBDS [4]

Answer:

$y\geq x-2$

$x+2y$

Step-by-step explanation:

step 1

Find the equation of the first inequality

Find the equation of the first solid line

we have the ordered pairs

(0,-2) and (2,0)

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The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute the values

$m=\frac{0+2}{2-0}$

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

$m=1$

The equation in slope intercept form is equal to

$y=mx+b$

we have

$m=1$

$b=-2$ ---> the y-intercept is given

substitute

$y=x-2$

Remember that

Everything to the left of the solid line is shaded

The inequality is

$y\geq x-2$

step 2

Find the equation of the second inequality

Find the equation of the second dashed line

we have the ordered pairs

(0,2) and (4,0)

Find the slope

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute the values

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

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

$m=-\frac{1}{2}$

The equation in slope intercept form is equal to

$y=mx+b$

we have

$m=-\frac{1}{2}$

$b=2$ ---> the y-intercept is given

substitute

$y=-\frac{1}{2}x+2$

Remember that

Everything below and to the left of the line is shaded

The inequality is

$y$

Rewrite

Multiply by 2 both sides

$2y$

$x+2y$

therefore

The system of inequalities is

$y\geq x-2$

$x+2y$

see the attached figure to better understand the problem

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3 years ago

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About 1,000 puzzle pieces

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2 years ago

In a certain function, y varies directly with x. If y = 6 when x = 8, find x when y = 9.

Hatshy [7]

If y = 6 when x = 8, then value of "x" when y = 9 is equal to 12

Solution:

Given that , In a certain function, y varies directly with x

And x = 8 when y = 6,

We have to find what will be the value of x when y = 9

Now, from the given information,

$\begin{array}{l}{y \alpha x} \\\\ {y=c x \rightarrow(1)}\end{array}$

where c is the proportionality constant

$\begin{array}{l}{\text { Now, substitute } x=8 \text { and } y=6 \text { in }(1)} \\\\ {\rightarrow 8=c(6) \rightarrow c=\frac{8}{6}} \\\\ {\rightarrow c=\frac{4}{3}} \\\\ {\text { Then, }(1) \rightarrow x=\frac{4}{3} y} \\\\ {\text { So, when } y=9} \\\\ {\rightarrow x=\frac{4}{3}(9)} \\\\ {\rightarrow x=4 \times 3} \\\\ {\rightarrow x=12}\end{array}$