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Solve the inequality for v.

9v-30≥5v-6
Simplify your answer as much as possible.

1 answer

To solve the inequality \( 9v - 30 \geq 5v - 6 \), follow these steps:

  1. Isolate the variable \( v \): First, we can get all terms involving \( v \) on one side of the inequality and constants on the other side. Subtract \( 5v \) from both sides:

    \[ 9v - 5v - 30 \geq -6 \]

    This simplifies to:

    \[ 4v - 30 \geq -6 \]

  2. Add 30 to both sides: Next, we add 30 to both sides to isolate the term with \( v \):

    \[ 4v - 30 + 30 \geq -6 + 30 \]

    This simplifies to:

    \[ 4v \geq 24 \]

  3. Divide by 4: Finally, divide both sides by 4 to solve for \( v \):

    \[ v \geq \frac{24}{4} \]

    This simplifies to:

    \[ v \geq 6 \]

Thus, the solution to the inequality is

\[ \boxed{v \geq 6} \]