Q4. - Algebra 1

Question

Read each question. Then fill in the correct answer on the answer document provided by your teacher or on a sheet of paper.

The highest score that is on record on a video game is 10,219 points. The lowest score on record is 257 points. Which of the following inequalities best shows the range of scores recorded on the game?

F $\mathit{x}\mathbf{\le }\mathbf{10}\mathbf{,}\mathbf{219}$

G $\mathit{x}\mathbf{\ge }\mathbf{257}$

H $\mathbf{257}\mathbf{<}\mathit{x}\mathbf{<}\mathbf{10}\mathbf{,}\mathbf{219}$

J $\mathbf{257}\mathbf{\le }\mathit{x}\mathbf{\le }\mathbf{10}\mathbf{,}\mathbf{219}$

Step-by-Step Solution

Answer

The inequality that best shows the range of scores recorded on the game is $\mathbf{257}\mathbf{\le }\mathit{x}\mathbf{\le }\mathbf{10}\mathbf{,}\mathbf{219}$. Therefore, the option J is correct.

Step 1. Write the inequality for the given problem.

It is given that the highest score is 10,219 points and the lowest score is 257 points.

Let $x$ be the score recorded on the game.

 

As, the highest score is 10,219 points. Therefore, the score recorded on the game must be less than or equal to 10,219.

 

Therefore, $x\le 10,219$

 

As, the lowest score is 257 points. Therefore, the score recorded on the game must be greater than or equal to 257.

 

Therefore, $x\ge 257$

 

Therefore, the inequality for the given problem is:

$x\ge 257$ and $x\le 10,219$

Step 2. Find the inequality that best shows the range of scores recorded on the game.

The inequality for the given problem is:

$x\ge 257$ and $x\le 10,219$

Therefore, the inequalities $x\ge 257$ and $x\le 10,219$ can be written as:

$257\le x\le 10,219$

Therefore, the inequality that best shows the range of scores recorded on the game is $257\le x\le 10,219$. Therefore, the option J is correct.