<span>The set <span>EE</span> is said to be bounded above if and only if there is an <span><span>M∈R</span><span>M∈R</span></span> such that <span><span>a≤M</span><span>a≤M</span></span>for all <span><span>a∈E</span><span>a∈E</span></span>, in which case <span>MM</span> is called an upper bound of <span>EE</span>.A number <span>ss</span> is called a supremum of the set <span>EE</span> if and only if <span>ss</span> is an upper bbound of <span>EE</span> and <span><span>s≤M</span><span>s≤M</span></span> for all upper bounds <span>MM</span> of <span>EE</span> (In this case we shall say that <span>EE</span> has a finite supremum <span>ss</span> and write <span><span>s=supE</span><span>s=supE</span></span>.</span>
Let <span><span>E⊂R</span><span>E⊂R</span></span> be nonempty.
<span>the set <span>EE</span> is said to be bounded below if and only if there is an <span><span>m∈R</span><span>m∈R</span></span> such that <span><span>a≥m</span><span>a≥m</span></span> for all <span><span>a∈E</span><span>a∈E</span></span>, in which case <span>mm</span> is called a lower bound of the set <span>EE</span>.A number <span>tt</span> is called an infimum of the set <span>EE</span> if and only if <span>tt</span> is a lower bound of <span>EE</span> and <span><span>t≥m</span><span>t≥m</span></span> for all lower bounds <span>mm</span> of <span>EE</span>. In this case we shall say that <span>EE</span> has an infimum <span>tt</span> and write <span><span>t=infE</span></span></span>
The expression for the cost of Taxi B is 0.40<em>x</em> + 2.<em></em>The expression for the cost of Taxi A is 0.20<em>x</em> + 4. The inequality asks for when the cost of Taxi B will be greater than Taxi A, so you write it as 0.40<em>x </em>+ 2 > 0.20<em>x</em> + 4, or 0.20<em>x</em> + 4 < 0.40<em>x </em>+ 2.
The answer is B)0.20<em>x</em> + 4 < 0.40<em>x </em>+ 2.
