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Solve the compound inequality. And write the solution in interval notation.

$3v - 6 < 9$ or $4v - 3 < -23$

I've reduced both down to:

$v < 5$ or $v < -5$.

$(-∞,-5) ∪ (-∞,5)$

Is this correct?

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    That looks right- though are you sure you have the right inequalities to start with? It's an odd answer, since if $x<-5$, $x<5$, so you don't need both inequalities. Note that $(-\infty, -5) \cup (-\infty,5) = (-\infty, 5)$. – 2017-01-20

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In fact, it looks great: $$ 3 v - 6 < 9 \Longleftrightarrow 3 v < 9 - (- 6) (= 15) \Longleftrightarrow v < \frac{15}{3} (= 5) \Longleftrightarrow v \in (- \infty , 5) $$ and $$ 4 v - 3 < - 23 \Longleftrightarrow 4 v < - 23 - (- 3) (= - 20) \Longleftrightarrow v < \frac{- 20}{4} (= - 5) \Longleftrightarrow v \in (- \infty , - 5)\mbox{,} $$ so $$ 3 v - 6 < 9 \quad \mbox{ or } \quad 4 v - 3 < - 23 \qquad \Longleftrightarrow \qquad v \in (- \infty , 5) \cup (- \infty , - 5) = (- \infty , 5)\mbox{.} $$