1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Sergeu [11.5K]
3 years ago
12

Five times the sum of a number and 27 is greater than or equal to six times the sum of that

Mathematics
1 answer:
AleksAgata [21]3 years ago
6 0

The complete version of question:

<em>Five times the sum of a number and 27 is greater than or equal to six times the sum of that number and 26. What is the solution of this problem.</em>

Answer:

5\left(x+27\right)\ge \:6\left(x+26\right)\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\le \:-21\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:-21]\end{bmatrix}

Step-by-step explanation:

As the description of the statement is:

'<em>Five times the sum of a number and 27 is greater than or equal to six times the sum of that number and 26'.</em>

<em />

As

  • <em>Five times the sum of a number and 27  </em>is written as: 5(x + 27)
  • <em>greater than or equal </em>is written as:  \geq
  • <em>six times the sum of that number and 26'  </em>is written as: 6(x + 26)

so lets combine the whole statement:

<em />5\left(x\:+\:27\right)\ge \:6\left(x\:+\:26\right)<em />

solving

<em />5\left(x\:+\:27\right)\ge \:6\left(x\:+\:26\right)<em />

<em />5x+135\ge \:6x+156<em />

<em />5x+135-135\ge \:6x+156-135<em />

<em />5x\ge \:6x+21<em />

<em />5x-6x\ge \:6x+21-6x<em />

<em />-x\ge \:21<em />

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

<em />\left(-x\right)\left(-1\right)\le \:21\left(-1\right)<em />

<em />x\le \:-21<em />

Therefore,

5\left(x+27\right)\ge \:6\left(x+26\right)\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\le \:-21\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:-21]\end{bmatrix}

You might be interested in
Which inequality is a true statement?
lubasha [3.4K]

9514 1404 393

Answer:

  • -3 ≤ -1
  • -3 < -1

Step-by-step explanation:

Negative three is less than (<) negative one, so any statement saying otherwise is incorrect. Correct choices are ...

  -3 ≤ -1

  -3 < -1

7 0
3 years ago
Equations
Flauer [41]

Answer:

Step-by-step explanation:

-3x + 4y = -18

8x - 4y =   28

5x = 10

x = 2

4 - y = 7

-y = 3

y = -3

(2, -3)

8 0
3 years ago
Read 2 more answers
The temperature is 45°F. The temperature will decrease by 2°F each hour. Let h be the number of hours.
Varvara68 [4.7K]
45 - 2t < 32 ( where t is time and you can replace it with x or h if you prefer)
Solving for t you get:
45 - 2t - 32 < 0
45 - 32 < 2t
13 < 2t
13/2 < t
Or the temperature will drop below 32F after 6 and a half hours
8 0
3 years ago
Write an expression that shows how to usethe halving and doubling strategy to find 8 x 50
faust18 [17]
Double of 50 is 100, so 28*100=2800, now half of the answer is 2800/2=1400
3 0
3 years ago
Find the number of turns or bumps in the graph of the function f(x) = x² - 25
Papessa [141]

Answer:

1 turn

Step-by-step explanation:

this is what the graph would look like:

4 0
2 years ago
Other questions:
  • 4y^2-16 is that a square of the sum, square of a difference, a product of a sum and difference, or not a special product?
    9·1 answer
  • Angles 1 and 2 are supplementary. If &lt;1 measures 116 degress, what is the measure of &lt;2
    7·2 answers
  • Gabriel invested $540 in an account paying an interest rate of 6.4% compounded monthly. Assuming no deposits or withdrawals are
    8·1 answer
  • a resteraunt owner earns 2.73$ profit per chicken tender plate, p, and 3.21$ profit per chicken tender salad, s. If a customer w
    12·1 answer
  • How do you solve 21r &lt; 7?
    13·2 answers
  • Lines P and Q are parallel. What is the measure of angle 1
    13·1 answer
  • Can someone please help me out ~ASAP~.
    15·1 answer
  • Help, I'm so confused I would love an explanation.
    8·2 answers
  • Pls help I really need it
    6·1 answer
  • Find the unknown side length of the rectangle is 3 2/3 and if the area is 11m2
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!