Chapter 5.7, Problem 37E

To determine

To find: how linear equation and inequalities are similar and different.

Answer to Problem 37E

The linear equation uses a solid line and linear inequality used a dashed line.

Explanation of Solution

Given:

Linear equation and linear inequalities.

Concept used:

Linear equation has one solution whereas linear inequality has many solutions.

Linear equation forma line as solution and linear inequality solution is represented by the area.

Calculation:

The following points represent some of the similarities and differences:

It looks all very similar and the algebraic manipulations remain the same while plotting the line but in inequality, it need to consider if the boundary line is dashed or solid depending on the inequality symbol used.

Ina linear equation, switching the sides do not affected on the equal sign but in linear inequality, switching sides brings in an Automatics change in signs, that is from greater than to less than and vice versa.

This is also happened when both sides of inequality are multiplies or divided by a negative number.

The solution of the linear equation gives an ordered pair while the solution of the linear inequality gives a region, either above or below the curve line.

Hence, linear equation uses a solid line and linear inequality used a dashed line.