All categories

3 years ago

What is the justification for each step in solving the inequality?

Mathematics

1 answer:

Fed [463]3 years ago

5 0

Step-by-step explanation:

$3x+\frac{5}{8}\geq 4x-\frac{1}{2}$

Subtract 5/8 on both sides

To subtract 5/8 we make the denominators same

$3x\geq 4x-\frac{1*4}{2*4}-\frac{5}{8}$

Addition or Subtraction property of order is used

$3x\geq 4x-\frac{9}{8}$

Subtract 4x on both sides

Addition or Subtraction property of order is used

$-x\geq -\frac{9}{8}$

Now divide both sides by -1

Multiplication or Division property of order is used

$\frac{-x}{-1} \geq \frac{-\frac{9}{8}}{-1}$

Multiplication or Division property of order is used

$x\leq \frac{9}{8}$

You might be interested in

Find Horizontal and Vertical asymptotes for y=(x^2 -9)/(4x^2 +1)

Gnom [1K]

Answer: Horizontal asymptote is $\dfrac{1}{4}$ and vertical asymptotes are $\pm \dfrac{1}{2i}$

Step-by-step explanation:

Since we have given that

$y=\dfrac{x^2-9}{4x^2+1}$

We need to find the horizontal and vertical asymptotes.

Since vertical asymptotes will occur where the denominator becomes zero.

So, here denominator is $4x^2+1$

Now,

$4x^2+1=0\\\\4x^2=-1\\\\x^2=\dfrac{-1}{4}\\\\x=\pm \dfrac{1}{2i}$

And the horizontal asympototes will occur when the coefficient of higher degree of numerator is divided by coefficient of higher degree of denominator.

$y=\dfrac{1}{4}$

Hence, horizontal asymptote is $\dfrac{1}{4}$ and vertical asymptotes are $\pm \dfrac{1}{2i}$

8 0

3 years ago

Which point would be a solution to the system of linear inequalities ?

brilliants [131]

Answer:

(12,-6)

Step-by-step explanation:

we have

$y\leq \frac{4}{3}x+5$ ----> inequality A

$y\geq -\frac{5}{2}x+5$ ---> inequality B

we know that

If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequalities (makes true both inequalities)

<u><em>Verify each point</em></u>

Substitute the value of x and the value of y of each ordered pair in the inequality A and in the inequality B

case 1) (0,-1)

Inequality A

$-1\leq \frac{4}{3}(0)+5$

$-1\leq5$ ----> is true

Inequality B

$-1\geq -\frac{5}{2}(0)+5$

$-1\geq 5$ ----> is not true

therefore

The ordered pair is not a solution of the system

case 2) (0,3)

Inequality A

$3\leq \frac{4}{3}(0)+5$

$3\leq5$ ----> is true

Inequality B

$3\geq -\frac{5}{2}(0)+5$

$3\geq 5$ ----> is not true

therefore

The ordered pair is not a solution of the system

case 3) (-6,-6)

Inequality A

$-6\leq \frac{4}{3}(-6)+5$

$-6\leq-3$ ----> is true

Inequality B

$-6\geq -\frac{5}{2}(-6)+5$

$-6\geq 20$ ----> is not true

therefore

The ordered pair is not a solution of the system

case 4) (12,-6)

Inequality A

$-6\leq \frac{4}{3}(12)+5$

$-6\leq21$ ----> is true

Inequality B

$-6\geq -\frac{5}{2}(12)+5$

$-6\geq -25$ ----> is true

therefore

The ordered pair is a solution of the system (makes true both inequalities)

8 0

3 years ago

How do I make a table for x = 2

postnew [5]

What kind of table?
Because for every the x would be 2

3 0

3 years ago

in slope intercept form, what is the equation of the line having a slope of 2 and passing through the point (6,24)?

Yanka [14]

Answer: y = 2x + 12

Explanation: The slope-intercept form is y = mx + b, where m is slope and b is the y-intercept. Substituting 2 for m, 6 for x, and 24 for y, we have 24 = 2(6) + b. Simplifying, we get that b = 12, so the equation is y = 2x + 12.

4 0

2 years ago

Read 2 more answers

Tamika has a spinner with 5 equal sections – red, blue, green, yellow, and purple. She plans to spin it 150 times. Predict how m

likoan [24]

If she would use it 150 times, the expected amount would be 60 times for it to land on yellow or green

8 0

2 years ago