Write the following as an inequality.
x is greater than or equal to -5 and less than 6
Use x only once in your inequality.
Answer (2)
Express 'x is greater than or equal to -5' as x ≥ − 5 .
Express 'x is less than 6' as x < 6 .
Combine the two inequalities into a single compound inequality: − 5 ≤ x < 6 .
The final answer is − 5 ≤ x < 6 .
Explanation
Understanding the Problem We need to translate the sentence 'x is greater than or equal to -5 and less than 6' into a single compound inequality using x only once.
Expressing the First Part 'x is greater than or equal to -5' can be written as x ≥ − 5 .
Expressing the Second Part 'x is less than 6' can be written as x < 6 .
Combining the Inequalities Combining these two inequalities, we get − 5 ≤ x < 6 . This means x is between -5 and 6, including -5 but not including 6.
Final Answer Therefore, the inequality representing the given sentence is − 5 ≤ x < 6 .
Examples
In real life, you might use inequalities to describe acceptable ranges. For example, a company might specify that a product's weight, x , must be greater than or equal to 50 grams and less than 60 grams. This can be written as 50 ≤ x < 60 . This ensures quality control by setting boundaries for acceptable values.
The inequality that represents 'x is greater than or equal to -5 and less than 6' is − 5 ≤ x < 6 . This means x can be any value from -5 to just below 6. The combined form effectively captures the range of values x can take.
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