Question

Write the inequality to describe the region between the \(yz\)-plane and the vertical plane \(x = 5\).

Short answer

The inequality to describe the region between the \(yz\)-plane and the vertical plane \(x = 5\)is \(0 < x < 5\).

Step-by-step solution

Simplify the equation.

\({R^3}\)is the three-dimensional coordinate system which contains\(x\),\(y\),and\(z\)-coordinates.

The equation \(x = 5\) in \({R^3}\) represents the set \(\{ (x,y,z)\mid x = 5\} \), which is the set of all points in \({R^3}\) whose \(x\) coordinate is 5 and \(y\),\(z\)-coordinates are any values.

Sketch the equation

The equation \(x = 5\) in is sketched.

But, the region between the \(yz\)-plane and the vertical plane \(x = 5\)describes all points whose \(x\)-coordinate is between 0 and 5, which is \(0 < x < 5\).

Thus, the inequality to describe the region between the \(yz\)-plane and the vertical plane \(x = 5\)is \(0 < x < 5\).