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Alekssandra [29.7K]
3 years ago
11

What is the solution to the inequality? 5(x−2)<−3x+6

Mathematics
1 answer:
goldfiish [28.3K]3 years ago
5 0

Answer:

x<2

Step-by-step explanation:

multiply 5 by the numbers inside the parenthesis

5x-10<-3x+6

add 10 to both sides

5x-10+10<-3x+6+10

simplify

5x<-3x+16

add 3x to both sides

5x+3x<-3x+16+3x

simplify

8x<16

divide by 8

8x/8 < 16/8

x<2

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How many times bigger is 5 with an exponent of 26 compared to 5 with an exponent of 22?
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Step-by-step explanation:

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Two payment options to rent a car: You can pay $20 a day plus 25¢ a mile (Option A) or pay $10 a day plus 50¢ a mile (Option B).
BaLLatris [955]

You must drive more than 40 miles to make option A the cheaper plan

<em><u>Solution:</u></em>

Two payment options to rent a car

Let "x" be the number of miles driven in one day

<em><u>You can pay $20 a day plus 25¢ a mile (Option A)</u></em>

25 cents is equal to 0.25 dollars

OPTION A :  20 + 0.25x

<em><u>You pay $10 a day plus 50¢ a mile (Option B)</u></em>

50 cents equal to 0.50 dollars

Option B: 10 + 0.50x

<em><u>For what amount of daily miles will option A be the cheaper plan ?</u></em>

For option A to be cheaper, Option A must be less than option B

Option A < Option B

20 + 0.25x < 10 + 0.50x

Solve the inequality

Add -0.50x on both sides

20 +0.25x -0.50x < 10 + 0.50x - 0.50x\\\\20 - 0.25x < 10

Add - 20 on both sides,

20 - 0.25x - 20 < 10 - 20\\\\-0.25x < -10

\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}

0.25x > 10

Divide both sides by 0.25

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7 0
3 years ago
If the car dealer pays 85% of the base price and 75% of the installed options price from the manufacturer,
stira [4]

Answer:

$18,007,50

Step-by-step explanation:

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Third, you have to add the 85% of the base price plus the 75% of the installed options that the dealer has to pay and you also have to add the destination charge of $285:

$15,937.5+$1,785+$285= $18,007.5

According to this, the dealer has to pay $18,007.5 for the car with a base price of $18,750 and installed options price $2380  including a destination charge of $285.

7 0
3 years ago
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