What is the largest integer value of $x$ for which $5-4x>17$?
Adding $4x$ to both sides, we have $5 > 17+4x$. Then, subtracting $17$ from both sides, we have $-12 > 4x$. Finally, dividing both sides by $4$, we have $-3 > x$. This inequality states that $x$ is strictly less than $-3$. The largest integer satisfying that condition is $\boxed{-4}$.
-4
Level 4
Prealgebra
Problem: What is the largest integer value of $x$ for which $5-4x>17$?
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To solve the inequality \(5 - 4x > 17\), we first isolate the term involving \(x\). We start by subtracting 5 from both sides of the inequality:

\(-4x > 17 - 5\)

This simplifies to:

\(-4x > 12\)

Next, we divide both sides by -4. It is important to remember that when dividing or multiplying both sides of an inequality by a negative number, the direction of the inequality sign must be reversed:

\(x < \frac{12}{-4}\)

Calculating the right side gives:

\(x < -3\)

The inequality indicates that \(x\) can take any value less than -3. The largest integer that satisfies this condition is -4. Thus, the final answer is -4.<|END_OF_LATENT|> The final answer is $-4$.