Solve the inequality 2 - 5n ≤ 37.
Understand the Problem
The question is asking to solve the inequality 2 - 5n ≤ 37 and then graph the solution on the number line provided.
Answer
The solution is $n \geq -7$.
Answer for screen readers
The solution to the inequality is $n \geq -7$.
Steps to Solve
- Isolate the variable term
To start solving the inequality $2 - 5n \leq 37$, subtract 2 from both sides:
$$ -5n \leq 37 - 2 $$
- Simplify the inequality
Now simplify the right side:
$$ -5n \leq 35 $$
- Divide by -5
Next, divide both sides by -5. Remember, when you divide by a negative number, the inequality sign reverses:
$$ n \geq -7 $$
- Graph the solution on the number line
To graph $n \geq -7$, place a solid dot on -7 (indicating that -7 is included in the solution) and shade everything to the right of -7.
The solution to the inequality is $n \geq -7$.
More Information
This means that any value of $n$ greater than or equal to -7 satisfies the inequality. The graph shows all these values on the number line.
Tips
- Forgetting to reverse the inequality sign when dividing by a negative number.
- Misplacing the solid dot on the number line; ensure to include -7 since it's part of the solution.
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