Practice Solving Multi-Step Inequalities

\(\begin{aligned}-42v+33 & < 8v + 91 \\\\
-42v& < 8v+58 &(\text{Subtract } 33 \text{ from both sides}) \\\\
-50v & < 58 &(\text{Subtract } 8v \text{ from both sides})\\\\
50v& > -58&(\text{Multiply both sides by }-1)\\\\
v& > -\dfrac{29}{25}&(\text{Divide both sides by }50 \text{ and simplify})
\end{aligned}\)

In conclusion, the answer is \(v > - \dfrac{29}{25}\).

\(\begin{aligned}50q+43 & > -11q + 70 \\\\
50q& > -11q+27 &(\text{Subtract } 43 \text{ from both sides}) \\\\
61q & > 27 &(\text{Add } 11q \text{ to both sides})\\\\
q& > \dfrac{27}{61}&(\text{Divide both sides by }61
) \end{aligned}\)

In conclusion, the answer is \(q > \dfrac{27}{61}\).

\(\begin{aligned}-65y+19 & < -2y + 41 \\\\
-65y& < -2y+22 &(\text{Subtract } 19 \text{ from both sides}) \\\\
-63y & < 22 &(\text{Add } 2y \text{ to both sides})\\\\
63y& > -22&(\text{Multiply both sides by }-1)\\\\
y& > -\dfrac{22}{63}&(\text{Divide both sides by }63)
\end{aligned}\)

In conclusion, the answer is \(y > - \dfrac{22}{63}\).

\(\begin{aligned}-48t+2 & \leq -71t + 14 \\\\
-48t&\leq -71t+12 &(\text{Subtract } 2 \text{ from both sides}) \\\\
23t &\leq 12 &(\text{Add } 71t \text{ to both sides})\\\\
t&\leq\dfrac{12}{23}&(\text{Divide both sides by }23)
 \end{aligned}\)

In conclusion, the answer is \(t \leq \dfrac{12}{23}\).