2 - 5n ≤ 37
Understand the Problem
The question requires solving the inequality 2 - 5n ≤ 37 and interpreting the solution on a number line.
Answer
$n \geq -7$
Answer for screen readers
The solution to the inequality is $n \geq -7$.
Steps to Solve
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Isolate the variable term To isolate the term with $n$, start by subtracting 2 from both sides of the inequality: $$ 2 - 5n - 2 \leq 37 - 2 $$ This simplifies to: $$ -5n \leq 35 $$
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Divide by the coefficient of n Next, divide both sides of the inequality by -5. Remember, when dividing by a negative number, the inequality sign reverses: $$ n \geq -7 $$
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Write the solution The solution indicates that $n$ can take on any value greater than or equal to -7.
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Represent on a number line To represent the solution on the number line, draw a solid dot above -7 (indicating inclusivity) and shade the line to the right, indicating that all values greater than -7 are included.
The solution to the inequality is $n \geq -7$.
More Information
This inequality means that any number greater than or equal to -7 will satisfy the condition. This includes -7 itself as well as numbers like -6, -5, 0, and positive numbers.
Tips
- Forgetting to reverse the inequality sign when dividing by a negative number. Always remember: divide by a negative, flip the inequality!
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