To check Nia's solution \( v = -2.9 \), we can estimate by substituting a nearby whole number value into the original equation \( -1.98 = 5.2v + 13.1 \).
Nia's solution is close to \(-3\). We can use this for our estimation:
Substituting \( v = -3 \) into the right side of the equation:
\[ 5.2(-3) + 13.1 = -15.6 + 13.1 = -2.5 \]
Now we compare \( -2.5 \) with \( -1.98 \). Since \(-2.5\) is reasonably close to \(-1.98\), it suggests that \( v = -2.9 \) is a plausible solution.
Among the options provided, the expression that uses \( v = -3 \) is:
\(-3 = 5(-3) + 13\)
This simplifies to:
\[ -3 = -15 + 13 \implies -3 = -2 \text{ (which is not true)} \]
So while that option confirms Nia's rounding in a general way, it doesn't confirm \( v = -2.9 \).
The best approach for her quick check is:
\(-1 = 5(-2) + 13\)
This simplifies to:
\[ -1 = -10 + 13 = 3 \text{ (which is also not true)} \]
We appear to have the right reasoning, but let's double-check the last choice with:
Using \( v = -2 \):
Substituting into the equation:
\[ -1 = 5(-2) + 13 \implies -1 = -10 + 13 = 3 \text{ (still not true)} \]
Ultimately, we see that substituting \( v = -3 \) or \( -2 \) gets us reasonable approximations.
The option closest to a reasonable check for clarity, according to \( v = -2.9 \) being round, would be;
-2 = 5(-2) + 13, checking simply how \( -2 \) lines up against expected values.
Summary: All alternatives only give marginal estimates, rather than definitely solving it back effectively.
Conclusively, using the range around -3 gives good insights, but proper re-checking with -2 or values adjacent assures that \( v = -2.9 \) is reasonable, making -2 = 5(-2) + 13 the most relevant for positive assurance.
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