Mathematics, 30.07.2020 09:01 kingbob101

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

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Answer from: nathansnyder200

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

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

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

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