Jaime is preparing for a bicycle race . His goal is to bicycle an average of at least 280 miles per week for 4 weeks. He bicycled 240 miles the first week, 310 miles the second week , and 320 miles the third week.. Which inequality can be used to represent the number of miles,x Jaime could bicycle on the 4th week to meet his goal? (240+310+320)/(3)+xgeqslant 280 B) 240+310+320geqslant x(280) C) (240)/(4)+(310)/(4)+(320)/(4)+xgeqslant 280 D) 240+310+320+xgeqslant 4(280) A B C D

To find the correct inequality, we need to calculate the total miles Jaime needs to bike in 4 weeks to meet his goal of an average of at least 280 miles per week.<br /><br />First, let's calculate the total miles Jaime has biked in the first 3 weeks:<br />\[ 240 + 310 + 320 = 870 \]<br /><br />Next, let's calculate the total miles Jaime needs to bike in 4 weeks to meet his goal:<br />\[ 280 \text{ miles per week} \times 4 \text{ weeks} = 1120 \text{ miles} \]<br /><br />Now, let's set up the inequality to find the number of miles, \( x \), Jaime needs to bike in the 4th week:<br />\[ 870 + x \geq 1120 \]<br /><br />Simplifying this inequality, we get:<br />\[ x \geq 1120 - 870 \]<br />\[ x \geq 250 \]<br /><br />So, the correct inequality is:<br />\[ 870 + x \geq 1120 \]<br /><br />Now, let's compare this inequality with the given options:<br /><br />A) \(\frac{240+310+320}{3}+x\geqslant 280\)<br /><br />B) \(240+310+320\geqslant x(280)\)<br /><br />C) \(\frac{240}{4}+\frac{310}{4}+\frac{320}{4}+xqslant 280\)<br /><br />D) \(240+310+320+x\geqslant 4(280)\)<br /><br />Option D is the correct one:<br />\[ 240+310+320+x\geqslant 4(280) \]<br /><br />So, the correct answer is D.