To determine the integers whose product with [tex]\(-1\)[/tex] gives specific results, follow these steps:
(a) We want to find the integer whose product with [tex]\(-1\)[/tex] is [tex]\(-22\)[/tex]. Let's denote this integer by [tex]\( x \)[/tex].
[tex]\[
-1 \cdot x = -22
\][/tex]
To isolate [tex]\( x \)[/tex], we divide both sides of the equation by [tex]\(-1\)[/tex]:
[tex]\[
x = \frac{-22}{-1} = 22
\][/tex]
So, the integer whose product with [tex]\(-1\)[/tex] is [tex]\(-22\)[/tex] is [tex]\( 22 \)[/tex].
(b) Next, we need to find the integer whose product with [tex]\(-1\)[/tex] is [tex]\(37\)[/tex]. Let's denote this integer by [tex]\( y \)[/tex].
[tex]\[
-1 \cdot y = 37
\][/tex]
Again, we isolate [tex]\( y \)[/tex] by dividing both sides of the equation by [tex]\(-1\)[/tex]:
[tex]\[
y = \frac{37}{-1} = -37
\][/tex]
Thus, the integer whose product with [tex]\(-1\)[/tex] is [tex]\( 37 \)[/tex] is [tex]\(-37\)[/tex].
(c) Finally, we want to determine the integer whose product with [tex]\(-1\)[/tex] is [tex]\(0\)[/tex]. Let's denote this integer by [tex]\( z \)[/tex].
[tex]\[
-1 \cdot z = 0
\][/tex]
To find [tex]\( z \)[/tex], we divide both sides by [tex]\(-1\)[/tex]:
[tex]\[
z = \frac{0}{-1} = 0
\][/tex]
Therefore, the integer whose product with [tex]\(-1\)[/tex] is [tex]\( 0 \)[/tex] is [tex]\( 0 \)[/tex].
In summary, the integers whose products with [tex]\(-1\)[/tex] are [tex]\(-22\)[/tex], [tex]\(37\)[/tex], and [tex]\(0\)[/tex] are:
- For [tex]\(-22\)[/tex], the integer is [tex]\( 22 \)[/tex].
- For [tex]\(37\)[/tex], the integer is [tex]\(-37\)[/tex].
- For [tex]\(0\)[/tex], the integer is [tex]\( 0 \)[/tex].
