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3 years ago

2(2x - 8) > 4(3x - 12) Solve the inequality (Just like my previous problem) Make sure to show work!!

Mathematics

2 answers:

scZoUnD [109]3 years ago

8 0

2(2x-8)
2•2x=4x
2•-8= -16
So now 4x-16
Now divide both sides by 4
4x/4=x
-16/4=-4
X=-4

Zolol [24]3 years ago

5 0

Answer:

x < 8

Step-by-step explanation:

This is a special case, so at the end of the equation we'll flip the sign.

Distribute:

2 * 2x = 4x

2 * -8 = -16

4x - 16

4 * 3x = 12x

4 * -12 = -48

12x - 48

4x - 16 > 12x - 48.

Subtract 12 from both sides.

12 - 12 = 0

4x - 12x = -8x

-8x - 16 > -48

The additive inverse of subtraction is addition so do -16 + -48, which equals -64

-8x/-8 = x

-64/-8 = 8

Now this is where we flip our sign so here we go :)

x < 8

There.

Hope this helped and sorry if I'm wrong.

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Answer:

(A) The rate of change in the price of a bushel of corn in the current year is $7.

(B) The price of a bushel of corn in the current year is $2 more than the price of a bushel of corn in the previous year.

Step-by-step explanation:

The graph for the prices of different numbers of bushels of corn at a store in the current year is shown below.

Part A:

The rate of change in the price of a bushel of corn in the current year based upon the number of bushels is known as the slope of the line.

The formula to compute the slope is:

$\text{Slope}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Consider the ordered pairs: (4, 28) and (10, 70)

Compute the slope of the line as follows:

$\text{Slope}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$=\frac{70-28}{10-4}\\\\=\frac{42}{6}\\\\=7$

Thus, the rate of change in the price of a bushel of corn in the current year is $7.

Part B:

The data for the price of bushels in the previous year is as follows:

Number of Bushels Price

2 10

4 20

6 30

8 40

Compute the rate of change in the price of a bushel of corn in the previous year based upon the number of bushels as follows:

Consider the ordered pairs: (2, 10) and (6, 30)

$\text{Slope}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$=\frac{30-10}{6-2}\\\\=\frac{20}{4}\\\\=5$

The rate of change in the price of a bushel of corn in the previous year is $5.

Thus, the price of a bushel of corn in the current year is $2 more than the price of a bushel of corn in the previous year.

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3 years ago

Two consecutive odd integers are such that one-third the smaller is greater than one-seventh of the larger one by 6. Find the nu

vaieri [72.5K]

Answer:

the number is 33 and 35 respectively

Step-by-step explanation:

The computation is shown below:

Let us assume X and X + 2 are the two consecutive odd integers

Now the equation is

(X ÷ 3) = ((X + 2) ÷ 7) + 6

(X ÷ 3) = (X + 2 + 6 × 7) ÷ 7

(X ÷ 3) = (X + 2 + 42) ÷ 7

(X ÷ 3) = (X + 44) ÷ 7

Now do the cross multiplication

7X = 3(X + 44)

7X = 3X + 132

4X = 132

X = 33

And, X + 2 = 33 + 2 = 35

hence, the number is 33 and 35 respectively

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3 years ago

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Romashka-Z-Leto [24]

Answer:

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$x = 0$

$x - 4 = 0$

$\boxed{\green{x_{1} = 0. \: \: \: x_{2} = 4}}$

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