To solve the inequality \(-2(a-7)-3m \geq -31\), we will follow these steps.
Step 1: Distribute the \(-2\)
We start by distributing the \(-2\) across the expression \(a-7\).
\[ -2(a-7) = -2a + 14 \]
Now we can rewrite the inequality:
\[ -2a + 14 - 3m \geq -31 \]
Step 2: Combine like terms
Next, we can isolate the terms on the left side. We will first subtract \(14\) from both sides of the inequality:
\[ -2a - 3m \geq -31 - 14 \]
Calculating the right side gives us:
\[ -31 - 14 = -45 \]
So we have:
\[ -2a - 3m \geq -45 \]
Step 3: Isolate \( -3m \)
Now, let's isolate the term \(-3m\) by adding \(2a\) to both sides:
\[ -3m \geq 2a - 45 \]
Step 4: Solve for \(m\)
Next, we solve for \(m\) by dividing both sides by \(-3\). Remember that dividing by a negative number reverses the inequality sign:
\[ m \leq \frac{2a - 45}{-3} \]
This can also be rewritten as:
\[ m \leq -\frac{2a}{3} + 15 \]
Conclusion
The solution to the inequality \(-2(a-7) - 3m \geq -31\) is:
\[ m \leq -\frac{2a}{3} + 15 \]
This indicates that the value of \(m\) is less than or equal to \(-\frac{2}{3}a + 15\).
1 answer