2(8)-2(y) <br> Distributive property

Solve:

drek231 [11]

The solutions to the inequalities are x >1 and x < 6

<h3>How to solve the inequalities?</h3>

The inequality expression is given as:

-2x + 5 < 3x + 10

Collect the like terms in the above inequality

-2x - 3x < 10 - 5

Evaluate the like terms

-5x < 5

Divide by -5

x >1

Also, we have

5(x - 2) <3x + 2

Open the bracket

5x - 10 < 3x + 2

Evaluate the like terms

2x < 12

Divide by 2

x < 6

Hence, the solutions to the inequalities are x >1 and x < 6

Read more about inequalities at

brainly.com/question/24372553

#SPJ1

5 0

1 year ago

Working alone, Henry takes 3 hours less than Mary to clean the carpets in the entire office. Working together, they can clean th

Sati [7]

Answer:

It would take Henry 3 hours to clean the office carpets if Mary were not there to help

Step-by-step explanation:

Assume that it takes Henry t hours to clean the carpets

∵ Henry takes 3 hours less than Mary to clean the carpets

∵ Henry takes t hours

- That means add 3 to t to find Mary time

∴ Mary takes t + 3 hours

∵ The rate of Henry is $\frac{1}{t}$

∵ The rate of Mary is $\frac{1}{t+3}$

∵ Working together, they can clean the carpets in 2 hours

- Add the two rates and equate the answer by $\frac{1}{2}$ (their rate together)

∴ $\frac{1}{t}+\frac{1}{t+3}=\frac{1}{2}$

Multiply the two denominators and multiply each numerator by the other denominator to add the two fractions of the left hand side

∵ $\frac{(1)(t+3)}{t(t+3)}+\frac{(1)t}{t(t+3)}=\frac{1}{2}$

∴ $\frac{(t+3)}{t(t+3)}+\frac{t}{t(t+3)}=\frac{1}{2}$

- Add the two fractions in the left hand side

∴ $\frac{t+3+t}{t(t+3)}=\frac{1}{2}$

∴ $\frac{2t+3}{t^{2}+3t}=\frac{1}{2}$

Use the cross multiplication

∵ (t² + 3t)(1) = 2(2t + 3)

∴ t² + 3t = 4t + 6

- Subtract 4t from both sides

∴ t² - t = 6

- Subtract 6 from both sides

∴ t² - t - 6 = 0

- Factorize it into two factors

∴ (t - 3)(t + 2) = 0

Equate each factor by 0 to find t

∵ t - 3 = 0

- Add 3 to both sides

∴ t = 3

OR

∵ t + 2 = 0

- Subtract 2 from both sides

∴ t = -2 ⇒ reject this answer because there is no - ve time

∴ t = 3

∴ Henry would take 3 hours to clean the carpets alone

It would take Henry 3 hours to clean the office carpets if Mary were not there to help

8 0

2 years ago

Avery got on the bus at 1:25 P.M. The trip took 74 minutes. Then she walked for 61 minutes to get home.

AnnZ [28]

Answer:

3:40 p.m.

Step-by-step explanation:

Add 74 minutes to 1:25 p.m.; the improperly formed result witll be 1:99 p.m.; to express this properly, add 1 hour to this time and subtract 60 minutes from it:

2:39 p.m. (time at which Avery gets off the bus)

If Avery walked 61 minutes to get home and we want to know what time she arrived, we add 61 minutes to 2:39 p.m., obtaining 2:100 p.m., which must in turn be re-written as 3:40 p.m.

Avery arrived home at 3:40 p.m.

Note: another way in which to do this problem is to add 74 minutes and 61 minutes, obtaining 135 minutes, and then adding 135 minutes to 1:25 p.m. and making the necessary adjustments to the result:

1:25 p.m. + 135 minutes = 1:160 p.m., or (recognizing that 120 min = 2 hours)

3:40 p.m.

6 0

2 years ago

A) Show work, b) solve, and c) graph the solutions for −7+2x>−27

8_murik_8 [283]

Answer:

x > -10

Step-by-step explanation:

−7+2x>−27

Add 7 to each side

−7+7+2x>−27+7

2x > -20

Divide each side by 2

2x/2 > -20/2

x > -10

7 0

2 years ago

Read 2 more answers

Using long division, you can calculate that f(x)=( 2x^3 + 14x^2 + 7x - 29 ) / (2x^2 + 5 ) = Q(x) + ( R(x) / (2x^2 +5) )

dusya [7]

Answer:

The Quotient Q(x) is (x + 7)

The Remainder R(x) is (2x - 64)

Limit as x approaches negative or positive infinity (R(x)/(2x² + 5)) is 0

Step-by-step explanation:

We want to use long division to determine the remainder and quotient in

(2x³+ 14x² + 7x - 29) / (2x² + 5)

This would be done step by step, as follows:

The denominator is written outside, and the numerator inside

We look for a number the when multiplied by the first expression of the funtion outside, gives the first expression of the funtion inside.

We multiply this function by the function outside, and write the resulting values under and subtract from the function inside.

The result is written, and the process is repeated, until the highest power of the function outside is greater the highest power of the function inside.

NOW, LET'S DO IT!

x times 2x = 2x³, so we choose x.

............... x

................................................

2x² + 5 | 2x³+ 14x² + 7x - 29

..............| 2x³ + 5x

..............| 14x² + 2x - 29

7 times 2x² gives 14x², we choose 7

...............x + 7

................................................

2x² + 5 | 2x³+ 14x² + 7x - 29

..............| 2x³ + 5x

..............| 14x² + 2x - 29

..............| 14x² + 35

..............| 2x - 64

We can't go further as the power of x inside is smaller than the power of x outside.

Therefore

Quotient Q(x) = x + 7

Remainder R(x) = 2x - 64

Limit as x approaches negative or positive infinity (R(x)/(2x² + 5))

= lim(x->±infty) (2x - 64) / (2x² + 5)

= 2lim(x->±infty) x(1 - 32/x) / x²(2 + 5/x²)

= 2(0)

= 0

4 0

2 years ago

2(8)-2(y) Distributive property