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Naily [24]
10 months 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]10 months 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:

Los números decimales son una combinación de números enteros y números que se encuentran entre los números enteros. A veces es importante poder comparar decimales para saber cuál es mayor. Por ejemplo, si alguien corrió los 100 metros planos en 10.57 segundos, y alguien más los corrió en 10.67 segundos, puedes comparar los decimales para determinar qué tiempo es más rápido. Saber cómo comparar decimales requiere el entendimiento del valor de posición decimal, y es similar a comprar números enteros.

 

Cuando trabajamos con decimales, hay veces que no se necesita un número preciso. En tal caso, es útil redondear números decimales. Por ejemplo, si la bomba de una gasolinera muestra que llenaste el tanque del carro de un amigo con 16.478 galones de gasolina, podrías querer redondear el número y decirle a tu amigo que le pusiste 16.5 galones.

Step-by-step explanation:

Otra forma de comparar decimales es comparar los dígitos en cada número, empezando con el lugar de posición mayor, que es el de la izquierda. Cuando un dígito en un número decimal es mayor que el dígito correspondiente en el otro número, entonces ése número decimal es mayor.

 

Por ejemplo, primero compara los dígitos de las décimas. Si son iguales, continúa con el lugar de las centésimas. Si esos dígitos no son iguales, el decimal con el dígito mayor es el número decimal mayor. Observa cómo se hace esto en los ejemplos siguientes.

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Sonya wants to sew ribbon along each side of a square pillow.
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We are given area of the ribbon = 144 square inches.

We know formula for side of a square = \sqrt{Area \ of \ a \ square }.

Plugging value of area in the formula, we get

Side of the square = \sqrt{144}

= 12 inches.

Sonya wants to sew ribbon along each side of a square pillow.

So, we need to find the perimeter of the square pillow.

<h3>Perimeter = 4 × side = 4 × 12 = 48 inches.</h3><h3>Therefore, she buy 48 inches of ribbon to have the exact amount that she needs.</h3>
5 0
3 years ago
1. Candace has $15 more than Amar. Their combined money totals $85. Which system of equations represents this situation? F. c +
ollegr [7]
The answer would be C+A= $85 or A+C=$85

Explanation: Candaces total money + Amar’s total money equals out to $85, it can be wrote either way and still equal $85.
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2 years ago
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ruslelena [56]

Answer:

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The sum of the 3 angles in a triangle = 180°

subtract the sum of the 2 given angles from 180° for missing angle

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5 0
3 years ago
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