Question

Knowing that 6 < x < 7 and 10 < y < 12, find the possible values of
x + y, y - x, xy, y/x

Answer 1

Answer:

x+y:

16<x+y<19

y-x:

3<y-x<6

xy:

60<xy<84

y/x:

10/7<y/x<2

Step-by-step explanation:

For x+y, it'll be

  6<x<7

+

  10<y<12

=16<x+y<19

____

y-x:

  10<y<12

--

  6<x<7

because of the negative sign the x inequality is reversed so it is -7<x<-6

and then you do the math and get 3<y-x<5

________

xy:

   10<y<12

x

   6<x<7

you multiply and get 60<xy<84

________

y/x:

  10<y<12

divided by

  6<x<7

now what you do is you have to switch around the signs for the x inequality and everything becomes its reciprocal. So the x inequality becomes 1/7<1/x<1/6 and then you multiply and get 10/7<y/x<12/6

Please give me a brainliest award. This took so long. I hope this helped.

Answer 2

Inequalities are used to make non-equal comparisons between two expressions. The inequality signs are: $\ne, >, <, \ge, \le$.

The solutions and possible values to the inequalities are:

$16 < x + y < 19$  $\to$ $x + y= \{17,18\}$

$4 < y - x < 5$  $\to$   $y - x = \{4.5, ...,4.9\}$

$60 < xy < 84$   $\to$ $xy = \{61,62,...83\}$

$1.67 < \frac{y}{x} < 1.71$  $\to$  $\frac{x}{y} = \{1.67,1.68...1.70\}$

Given that:

$6 < x < 7$ and $10 < y < 12$

To calculate the possible values of $x + y$, we simply add both inequalities; i.e.

$(6 < x < 7) + (10 < y < 12)$

This gives:

$6 + 10 < x + y < 7 + 12$

$16 < x + y < 19$

This means that the possible values of $x + y$ are between 16 and 19 (both exclusive). So, some possible values are:

$x + y= \{17,18\}$

To calculate the possible values of $y - x$, we simply subtract the inequality of x from y; i.e.

$(10 < y < 12) - (6 < x < 7)$

This gives:

$10 - 6 < y - x < 12 - 7$

$4 < y - x < 5$

This means that the possible values of $y - x$ are between 4 and 5 (both exclusive). So, some possible values are:

$y - x = \{4.5, ...,4.9\}$

To calculate the possible values of $xy$, we simply multiply both inequalities. i.e.

$(6 < x < 7) \times (10 < y < 12)$  

This gives:

$6 \times 10 < x \times y < 7 \times 12$

$60 < x \times y < 84$

$60 < xy < 84$

This means that the possible values of $xy$ are between 60 and 84 (both exclusive). So, some possible values are:

$xy = \{61,62,...83\}$

To calculate the possible values of $\frac{y}{x}$, we simply divide the inequality of y by x. i.e.

$(10 < y < 12) \div (6 < x < 7)$

This gives:

$\frac{10}{6} < \frac{y}{x} < \frac{12}{7}$

$1.67 < \frac{y}{x} < 1.71$

This means that the possible values of $\frac{y}{x}$ are between 1.67 and 1.71 (both exclusive). So, some possible values are:

$\frac{x}{y} = \{1.67,1.68...1.70\}$

Hence, the solutions and possible values to the inequalities are:

$16 < x + y < 19$  $\to$ $x + y= \{17,18\}$

$4 < y - x < 5$  $\to$   $y - x = \{4.5, 4.9...\}$

$60 < xy < 84$   $\to$ $xy = \{61,62,...83\}$

$1.67 < \frac{y}{x} < 1.71$  $\to$  $\frac{x}{y} = \{1.67,1.68...1.70\}$

Read more about inequalities:

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