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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):

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Answer:

7/8 > 5/6

Step-by-step explanation:

A) 7/8

We can compare this as follows.

Lets say both are equal.

Cross multiplying these we get 40=42

We get 40<42. In fraction we get

In case if you want to convert this to decimal, we get;

5/6 = 0.833 and 7/8 = 0.875

We get 5/6<7/8

B) 4/5

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C) 3/4

we get 3/4 = 0.75 and 5/6 = 0.833

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D) 2/3

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Step-by-step explanation:

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3 years ago
Ben's living room is a rectangular measuring 12 yards x 204" by how many feet does the length of the room exceed the with the le
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Answer:

The length of the room exceeds the width by 19 feet

Step-by-step explanation:

From the question, the room measures 12 yards x 204", that 12 yards x 204 inches. To determine by how many feet the length of the room exceeds the width, we will first convert both units of measurement ( yards and inches) to feet.

To convert 12 yards to feet,

1 yard = 3 feet

∴ 12 yards will be 3 × 12 feet = 36 feet

To convert 204" to feet

12" = 1 foot

∴ 204" will be 204/12 feet = 17 feet

Hence, the room measures 36 feet × 17 feet

That is, Length of the room = 36 feet

and width of the room = 17 feet

Now, to determine by how many feet the length of the room exceeds the width, we will deduct the width of the room from the length of the room, that is,

36 feet - 17 feet = 19 feet

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The line graph shows the average number of awakenings during the night for men and women of different ages. Use the graph to est
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*see attachment showing the line graph

Answer:

2

Step-by-step explanation:

The red line represents the line for women, while the blue line represents the line for men.

Age 45 is the middle of 40 and 45 on the x-axis.

The average number of awakenings during the night for 45 ​-year-old men ≈ 5

The average number of awakenings during the night for 45 ​-year-old women = 3

The difference = 5 - 3 = 2 times during the night.

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Need help on doing the work to figure out how music hour she took
Rzqust [24]

Answer:

D 1/27 hour per question

Step-by-step explanation:

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1/3 ÷ 9

Copy dot flip

1/3 * 1/9

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8 0
3 years ago
Read 2 more answers
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