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
Naily [24]
1 year ago
14

Solve the inequality both algebraically and graphically. Draw a number line graph of the solution and give interval notation.

Mathematics
1 answer:
Lemur [1.5K]1 year ago
4 0
Finding the solution algebraically

To answer this inequality, we can follow the next steps:

1. Multiply by 7 both sides of the inequality:

7\cdot\frac{(x-7)}{2}

2. Multiply by 2 both sides of the inequality:

7\cdot2\cdot^{\cdot}\frac{(x-7)}{2}

3. Apply the distributive property at the left side of the inequality:

7\cdot x-7\cdot7

4. Add 49 to both sides of the inequality:

7x-49+49

5. Finally, divide both sides of the inequality by 7:

\frac{7x}{7}

We can graph this inequality in the number line as follows:

Notice the parenthesis indicating that the solution is the number below 131/7 (but not equal to 131/7). <em>In interval notation the solution is</em>:

(-\infty,\frac{131}{7})(-\infty,18\frac{5}{7})

Or, approximately:

(-\infty,18.7142857143)

The number 131/7 in decimal is equivalent to 18.7142857143, so the graph of the solution is given by graph A (we can see that there are seven divisions between 18 and 19; since we have that the shaded division is in the 5th division, then, we have 5/7 = 0.714285714286, that is, the decimal part of the above number).

We can express the number 131/7 as a mixed number as follows:

\frac{131}{7}=\frac{126}{7}+\frac{5}{7}=18+\frac{5}{7}=18\frac{5}{7}

Again, <em>notice also the symbol for the left part of the interval notation is a parenthesis since the interval is open at the point 131/7 = 18 + 5/7</em>.

Finding the solution graphically

To find the solution graphically, we can represent the inequality as two lines as follows:

y=\frac{x-7}{2},y=\frac{41}{7}

Then, if we graph the first line, we can find the x- and the y-intercepts to find two points to graph the line. We have that the x- and the y-intercepts are:

The x-intercept is (that is, when y = 0):

0=\frac{x-7}{2}\Rightarrow x-7=0\Rightarrow x=7

Then, the x-intercept is (7, 0), and the y-intercept (the point on the graph when x = 0) is:

y=\frac{x-7}{2}\Rightarrow y=\frac{0-7}{2}\Rightarrow y=-\frac{7}{2}

Then, the y-intercept is (0, -7/2).

The other line is given by:

y=\frac{41}{7}=\frac{35}{7}+\frac{6}{7}=5\frac{6}{7}

With this information, we can graph both lines:

And we can see that the point where the two lines coincide is:

(\frac{131}{7},\frac{41}{7})

Then, <em>the values for x of the line (x-7)/2 [that is, the values of y = (x-7)/2] that are less than y = 41/7, represented as</em>:

\frac{(x-7)}{2}

Are those values of x less than 131/7, or the solution is also (we express the solution as a fraction or a mixed number as follows) (the same solution):

(-\infty,\frac{131}{7})or(-\infty,18\frac{5}{7})

In summary, we have that the solution to the inequality is:

As an inequality:

x

In interval notation:

(-\infty,18\frac{5}{7})or(-\infty,\frac{131}{7})

And the representation of the solution on the number line is (option A):

You might be interested in
Find the length of the hypotenuse of an isosceles right triangle whose legs are 1 unit in length.
stiks02 [169]

check the picture below

and isosceles triangle, has two equal sides, thus, sides "a" and "b" for the triangle to be an isosceles, have to be equal

6 0
3 years ago
Read 2 more answers
ATTENTION WORTH 50 POINTS! I will award brainliest to whoever answers within 30 minutes and is the first answer!!! Thanks!
Nutka1998 [239]
Sweet................
a. (0,4500) initial height
b. take any to points and find slope which is rate in ft per min and is also negative in this case
c. (3,0) hits ground after 3 minutes
d. after b, use y-y1=m (x-x1) for any point (x1,y1)
ur welcome. plz follow
7 0
3 years ago
Emilio has 5 bags of birdseed .Each bag has about 28 ounces of birdseed . If he divides the birdseed equally into 3 containers ,
MrMuchimi

Answer:

total ounces of birdseed = 5*28=140

number of birdseed of a container = 140/3 = 46.6666 ounces =140/3 ounces

he will put 140/3 ounces in each container


8 0
3 years ago
The number divided by -4 is increased by -63, the result is -45. What is the number? 
Pavlova-9 [17]
X / (-4) + ( -63) = -45 <=> x / ( -4) = 63 - 45 <=> x / (-4) = 18 <=> x = 18 * (-4) <=> x = -72.
3 0
3 years ago
Read 2 more answers
Someone pls anwser this.​
Orlov [11]

Answer:

YES, HAVE A GREAT DAYYYYYYYYYYYY!!!

Step-by-step explanation:

THX 4 THE POINTS!!!!!

3 0
3 years ago
Read 2 more answers
Other questions:
  • Each of the following statements describes a quadrilateral. Which of the quadrilaterals are NOT parallelograms? Choose three.
    9·2 answers
  • Describe how to determine the average rate of change between x=1 and x=3 for the function f(x)=3x^3+1 include the average rate o
    6·1 answer
  • Find the area of the trapezoid
    5·1 answer
  • Need help pleaseeeeeeeeeeee
    10·1 answer
  • Evaluate the expression when <br> =n8<br> .<br> −n216
    15·1 answer
  • What is -3 times x squared?
    9·1 answer
  • Help! how do I do this??
    8·2 answers
  • Alright one more question<br> whoever can answer this and the next question wins brainliest
    10·1 answer
  • !!!!!! hElP mE PleAsE !!!!!!
    13·2 answers
  • Evaluate x1 - x1 + x0 for x = 2.<br> 0<br> 1/2<br> 1 1/2<br> 2 1/2
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!