1Cademy - Translating and Solving $$143$$ is the product of $$-11$$ and $$y$$

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Translating and Solving ' $143$ is the product of $-11$ and $y$ '

To translate and solve the sentence "The number $143$ is the product of $-11$ and $y$ ," apply the systematic translation process:

Locate the "equals" word: The word "is" translates to an equals sign ( $=$ ).
Translate the left side: "The number $143$ " is simply $143$ .
Translate the right side: "The product of $-11$ and $y$ " uses the keyword product to signal multiplication, giving $-11y$ .

Combining these elements yields the equation $143 = -11y$ .

To solve the equation, isolate the variable by dividing both sides by $-11$ (the Division Property of Equality):

$\frac{143}{-11} = \frac{-11y}{-11}$

On the right side, $\frac{-11y}{-11} = y$ . On the left side, $\frac{143}{-11} = -13$ (a positive divided by a negative produces a negative quotient). The solution is:

$-13 = y$

Finally, verify by substituting $-13$ for $y$ in the original equation:

$143 \stackrel{?}{=} -11(-13)$

$143 = 143 \checkmark$

Because both sides are equal, $y = -13$ is confirmed as the correct solution. This example illustrates how the keyword "product" in a sentence signals a multiplication equation, which is then solved by dividing both sides by the negative coefficient.

Updated 2026-04-21

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OpenStax Elementary Algebra

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