Translating to an Inequality and Solving
Translating to an Inequality and Solving
To translate English sentences into inequalities, we need to recognize the phrases that indicate the inequality. Some words are easy, like ‘more than’ and ‘less than’. But others are not as obvious.
Think about the phrase ‘at least’ – what does it mean to be ‘at least 21 years old’? It means 21 or more. The phrase ‘at least’ is the same as ‘greater than or equal to’.
The table below shows some common phrases that indicate inequalities.
| \(>\) | \(\ge \) | \(<\) | \(\le \) |
|---|---|---|---|
| is greater than | is greater than or equal to | is less than | is less than or equal to |
| is more than | is at least | is smaller than | is at most |
| is larger than | is no less than | has fewer than | is no more than |
| exceeds | is the minimum | is lower than | is the maximum |
Example
Translate and solve. Then write the solution in interval notation and graph on the number line.
Twelve times c is no more than 96.
Solution
| Translate. | |
| Solve—divide both sides by 12. | |
| Simplify. | |
| Write in interval notation. | |
| Graph on the number line. | |
Example
Translate and solve. Then write the solution in interval notation and graph on the number line.
Thirty less than x is at least 45.
Solution
| Translate. | |
| Solve—add 30 to both sides. | |
| Simplify. | |
| Write in interval notation. | |
| Graph on the number line. |
This lesson is part of:
Solving Linear Equations II
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