Is the inequality true or false?
$-7 \leqslant-6$
The problem asks to evaluate the truth value of the inequality \(-7 \leq -6\). The symbol \(\leq\) denotes "less than or equal to," meaning the condition is satisfied if either the left number is strictly less than the right number, or if they are equal to each other.
To compare two negative integers like \(-7\) and \(-6\), we can visualize their positions on the real number line. The number \(-6\) is located to the right of \(-7\), which means that \(-6\) is greater than \(-7\), or equivalently, \(-7\) is less than \(-6\). Mathematically, we express this as \(-7 < -6\).
Since \(-7\) is strictly less than \(-6\), the condition \(-7 \leq -6\) is satisfied. Therefore, the given inequality is true.
Understanding inequalities is fundamental for comparing quantities in everyday life. For instance, if you have a budget of \(\$10\) and an item costs \(\$7\), you can represent this as \(7 \leq 10\), which is a true statement indicating that you have enough money to make the purchase. Similarly, negative numbers are used in temperature readings: if the temperature outside is \(-7^\circ C\), it is colder (lower) than a temperature of \(-6^\circ C\), illustrating the concept of \(-7 < -6\).