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3 years ago

Solve this please, Idk why it’s so hard for me? Thanks!!

Mathematics

2 answers:

tia_tia [17]3 years ago

8 0

Answer:

x = -10

Step-by-step explanation:

Solve for x:

(2 (6 x + 9))/3 + x = (2 (5 x - 10))/5 + 2 x

Put each term in (2 (6 x + 9))/3 + x over the common denominator 3: (2 (6 x + 9))/3 + x = (2 (6 x + 9))/3 + (3 x)/3:

(2 (6 x + 9))/3 + (3 x)/3 = (2 (5 x - 10))/5 + 2 x

(2 (6 x + 9))/3 + (3 x)/3 = (2 (6 x + 9) + 3 x)/3:

(2 (6 x + 9) + 3 x)/3 = (2 (5 x - 10))/5 + 2 x

2 (6 x + 9) = 12 x + 18:

(12 x + 18 + 3 x)/3 = (2 (5 x - 10))/5 + 2 x

Grouping like terms, 12 x + 3 x + 18 = (12 x + 3 x) + 18:

((12 x + 3 x) + 18)/3 = (2 (5 x - 10))/5 + 2 x

12 x + 3 x = 15 x:

(15 x + 18)/3 = (2 (5 x - 10))/5 + 2 x

Put each term in (2 (5 x - 10))/5 + 2 x over the common denominator 5: (2 (5 x - 10))/5 + 2 x = (2 (5 x - 10))/5 + (10 x)/5:

(15 x + 18)/3 = (2 (5 x - 10))/5 + (10 x)/5

(2 (5 x - 10))/5 + (10 x)/5 = (2 (5 x - 10) + 10 x)/5:

(15 x + 18)/3 = (2 (5 x - 10) + 10 x)/5

2 (5 x - 10) = 10 x - 20:

(15 x + 18)/3 = (10 x - 20 + 10 x)/5

10 x + 10 x = 20 x:

(15 x + 18)/3 = (20 x - 20)/5

Multiply both sides by 15:

(15 (15 x + 18))/3 = (15 (20 x - 20))/5

15/3 = (3×5)/3 = 5:

5 (15 x + 18) = (15 (20 x - 20))/5

15/5 = (5×3)/5 = 3:

5 (15 x + 18) = 3 (20 x - 20)

Expand out terms of the left hand side:

75 x + 90 = 3 (20 x - 20)

Expand out terms of the right hand side:

75 x + 90 = 60 x - 60

Subtract 60 x from both sides:

(75 x - 60 x) + 90 = (60 x - 60 x) - 60

75 x - 60 x = 15 x:

15 x + 90 = (60 x - 60 x) - 60

60 x - 60 x = 0:

15 x + 90 = -60

Subtract 90 from both sides:

15 x + (90 - 90) = -90 - 60

90 - 90 = 0:

15 x = -90 - 60

-90 - 60 = -150:

15 x = -150

Divide both sides of 15 x = -150 by 15:

(15 x)/15 = (-150)/15

15/15 = 1:

x = (-150)/15

The gcd of -150 and 15 is 15, so (-150)/15 = (15 (-10))/(15×1) = 15/15×-10 = -10:

Answer: x = -10

Stolb23 [73]3 years ago

6 0

I believe it is -19 not sure if that is the for sure answer

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Suppose you budgeted $2800 for fuel expenses for the year. How many miles could you drive if gas were $2.70 per gallon and your

Julli [10]

Answer:

29037.036 miles

Step-by-step explanation

There are two possible ways to solve this problem.

The first option starts with the $2800 dollars for the years. You first want to divide this by $2.70, because it will give you the amount of gallons of gas you can buy with that money.

2800/2.70 = 1037.037

This means you can buy 1037.037 gallons of gas in the year. Now you need to convert this to miles by multiplying by the amount of miles per gallon.

1037.037 x 28 = 29037.036 gallons

The second way to look at this is dimensional analysis. If you have learned this, then continue on reading this, but if you haven't I might only confuse you. I only suggest this because it can make it a little easier.

For the dimensional analysis, you need to start with what you are given and move to what you need to know, so you will start with the $2800 dollars and move to gallons. $2.70 per gallon and 28 miles per gallon are your conversion factors.

Set it up like this:

$2800 dollars * \frac{1 gallon}{2.70 dollars} * \frac{28 miles}{1 gallon} = 29037.036 miles$