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11 votes
Solve for v.
-3(v + 15) + 1 > 10

User Marilee
by
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2 Answers

6 votes
-3(v+15)+1>10
-3v-45+1>10
-3v-44>10
-3v>10+44
-3v>54
X<-18
User Omitobi
by
8.2k points
4 votes

Answer:

v < -18

Explanation:

You want the solution to -3(v +15) +1 > 10.

Simplify

Simplifying, we have ...

-3v -45 +1 > 10

-3v -44 > 10

Solve

Making the v-term positive, we get ...

-54 > 3v . . . . . . . . add 3v-10

-18 > v . . . . . . . divide by 3

The solution for v is v < -18.

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Additional comment

We could write the inequality as -3v > 54, then divide by -3. Doing that requires we reverse the inequality to v < -18. Sometimes that reversal is forgotten or confusing, so we choose to write the inequality in such a way that we don't need to reverse the symbol when we divide.

We like the final expression to involve the comparison symbols < or ≤, so the order of the variables and constants in that expression matches their order on the number line. Here, the variable v is on the left in v < -18, and the shaded portion is on the left of the boundary value -18 when we plot this on a number line.

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User Brendan Benson
by
8.5k points

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