Write the following as an inequality.
6 is greater than x, and x is greater than or equal to -2
Use x only once in your inequality.
Answer (2)
Express '6 is greater than x' as x < 6 .
Express 'x is greater than or equal to -2' as x ≥ − 2 .
Combine the two inequalities to get − 2 ≤ x < 6 .
The final inequality is − 2 ≤ x < 6 .
Explanation
Understanding the Problem We are given the sentence "6 is greater than x, and x is greater than or equal to -2" and we want to express this as a single inequality using x only once.
Expressing the First Part as an Inequality The first part of the sentence, "6 is greater than x", can be written as x"> 6 > x or equivalently as x < 6 .
Expressing the Second Part as an Inequality The second part of the sentence, "x is greater than or equal to -2", can be written as x ≥ − 2 .
Combining the Inequalities Now we combine these two inequalities. We have x < 6 and x ≥ − 2 . Combining these gives us − 2 ≤ x < 6 .
Final Answer Therefore, the inequality is − 2 ≤ x < 6 .
Examples
In real life, you might use inequalities like this to describe acceptable ranges for things. For example, if a store offers a discount for people aged between 18 and 65 (inclusive of 18, but not including 65), you could represent the eligible ages, x , with the inequality 18 ≤ x < 65 . This means someone aged 18 or older, but strictly younger than 65, qualifies for the discount.
The inequality representing "6 is greater than x, and x is greater than or equal to -2" is − 2 ≤ x < 6 . This indicates that x is at least -2 and less than 6. Combining these gives the complete range for x.
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