Question

for nitrogen to be a liquid, its temperature must be within 12.78 °f of -333.22 °f. the equation |x + 333.22| = 12.78 can be used to find x, which represents the maximum and minimum temperatures at which nitrogen is a liquid. is the maximum temperature at which nitrogen is a liquid. is the minimum temperature at which nitrogen is a liquid.

Explanation:

Step1: Understand the absolute - value equation concept

The equation \(|x - (- 333.22)|=12.78\) represents the distance of \(x\) from \(-333.22\) is \(12.78\). It can be split into two cases: \(x-(-333.22)=12.78\) and \(x - (-333.22)=-12.78\).

Step2: Solve for the maximum temperature

For \(x-(-333.22)=12.78\), simplify the left - hand side to get \(x + 333.22=12.78\). Then solve for \(x\): \(x=12.78-333.22=-320.44\).

Step3: Solve for the minimum temperature

For \(x-(-333.22)=-12.78\), simplify the left - hand side to get \(x + 333.22=-12.78\). Then solve for \(x\): \(x=-12.78-333.22=-346\).

Answer:

The maximum temperature is \(-320.44^{\circ}F\) and the minimum temperature is \(-346^{\circ}F\).