Answered

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Jana writes the true equation [tex]\((-9) - 8 = -17\)[/tex]. A second equation from the same fact family is shown:

[tex]\[
(-8) + \left(\_\right) = -17
\][/tex]

What value should Jana put in the blank to make the equation true?

A. [tex]\(-17\)[/tex]
B. [tex]\(17\)[/tex]
C. [tex]\(-9\)[/tex]
D. [tex]\(8\)[/tex]

Sagot :

GinnyAnswer
To solve the equation [tex]\((-8) + \left(\_\right) = -17\)[/tex], we need to determine the value that makes this equation true.

Let's denote the blank with [tex]\(x\)[/tex]. So, the equation becomes:
[tex]\[ (-8) + x = -17 \][/tex]

Our goal is to isolate [tex]\(x\)[/tex]. To do this, we can subtract [tex]\(-8\)[/tex] from both sides of the equation:
[tex]\[ (-8) + x - (-8) = -17 - (-8) \][/tex]

Simplifying this, we have:
[tex]\[ x = -17 - (-8) \][/tex]

We know that subtracting a negative is the same as adding the positive value of that number, so:
[tex]\[ x = -17 + 8 \][/tex]

Now, let's calculate [tex]\(-17 + 8\)[/tex]:
[tex]\[ -17 + 8 = -9 \][/tex]

Therefore, the value that Jana should put in the blank to make the equation [tex]\((-8) + \left(\_\right) = -17\)[/tex] true is [tex]\(-9\)[/tex].

Thus, the correct value is:
[tex]\[ \boxed{-9} \][/tex]
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