Q13. - Algebra 1

Question

The highest point in Kentucky is at an elevation of 4145 feet above sea level. The lowest point in the state is at an elevation of 257 feet above sea level. Write an inequality to describe the possible elevations in Kentucky.

Step-by-Step Solution

Answer

$\mathbf{257}\mathbf{\le }\mathit{x}\mathbf{\le }\mathbf{4145}$represent the possible elevation in Kentucky.

Step 1. Define ‘inequality’.

Inequality is an expression in which two numbers or any two terms are compared using less than $(<)$, greater than $(>)$, less than equal to $(\le )$ or greater than equal to $(\ge )$ signs.

Step 2. Write the inequalities.

Let $x$ represent the possible elevations in Kentucky.

The highest point in Kentucky is at an elevation of 4145 feet above sea level.

Thus, $x$ is lesser than or equal to the highest elevation.

That is,$x\le 4145 \dots \left(1\right)$ 

The lowest point in the state is at an elevation of 257 feet above sea level.

Thus, $x$ is greater than or equal to the lowest elevation.

That is, $x\ge 257$

That is, $257\le x \dots \left(2\right)$

Step 3. State the conclusion.

Combine the inequalities (1) and (2) to get the required in equality.

 $257\le x\le 4145$