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Determine the integer whose product with [tex]\((-1)\)[/tex] is:

(a) [tex]\(-22\)[/tex]

(b) [tex]\(37\)[/tex]

(c) [tex]\(0\)[/tex]


Sagot :

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].
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