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3 years ago

Solve 2(4 x + 3) < 5 x + 21. { x | x < 9} { x | x > -5} { x | x > -9} { x | x < 5}

Mathematics

1 answer:

Nesterboy [21]3 years ago

5 0

Answer:

x <5

Step-by-step explanation:

2(4 x + 3) < 5 x + 21

Distribute

8x +6 < 5x +21

Subtract 5x from each side

8x -5x +6 < 5x-5x+21

3x +6 < 21

Subtract 6 from each side

3x+6-6 <21-6

3x <15

Divide each side by 3

3x/3 <15/3

x <5

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3 years ago

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JulsSmile [24]

Let us check each Option :

$\mathsf{First\;Option : \left(\dfrac{m + 9}{m - 9}\right)\left(\dfrac{m + 9}{m - 9}\right)}$

$\mathsf{\implies \left(\dfrac{m + 9}{m - 9}\right)^2\;\neq\;1}$

$\mathsf{Second\;Option : \left(\dfrac{m + 9}{m - 9}\right)\left(\dfrac{m - 9}{m + 9}\right)}$

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$\mathsf{Third\;Option : \left(\dfrac{m + 9}{m - 9}\right)\left(\dfrac{9 + m}{9 - m}\right)}$

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$\mathsf{\implies-\left(\dfrac{m + 9}{m - 9}\right)\left(\dfrac{m + 9}{m - 9}\right)}$

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$\mathsf{Fourth\;Option : \left(\dfrac{m + 9}{m - 9}\right)\left(\dfrac{9 - m}{9 + m}\right)}$

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$\mathsf{\implies -\left(\dfrac{m + 9}{m - 9}\right)\left(\dfrac{m - 9}{9 + m}\right)}$

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<u>Answer</u> : Option (2)

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3 years ago

Help, help help. just give answers

Fynjy0 [20]

To solve this problem, there are a couple things we need to do. First of all, we need to figure out how much more she's running every day. On day 1, she ran 3/16 of a mile. On day 2, she ran 3/8 of a mile. On day 3, she ran 9/16 of a mile.

How much are we adding each time? To find that out, we need all of our fractions to have the same denominator so we can compare. Let's give 3/8 a denominator of 16. 8*2=16. What you do on one side of the fraction bar, you MUST do to the other: 3*2=6. So, 3/8 = 6/16.

Day 1: 3/16. Day 2: 6/16. Day 3: 9/16. Now do you see the pattern? Every day, she runs 3/16 of a mile more. That's the answer to part 1: 3/16.

So, how long will it take her to get over 1 mile? Let's continue. Day 3: 9/16. Day 4: 9+3=12, so that's 12/16. Day 5: 15/16. Day 6: 18/16! Since the numerator is bigger than the denominator, guess what? That's more than one mile!! So on the 6th time she runs, she ran 18/16 miles. Keep in mind that 18/16 = 9/8 = 1 1/8 miles.

Answers: 3/16; 6th; 1 1/8 (or 9/8)

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