Problem 113 - College Algebra

Question

Describe ways in which solving a linear inequality is similar to solving a linear equation.

Step-by-Step Solution

Answer

Solving linear inequalities is similar to solving linear equations in the sense that both involve identifying the variable, simplifying both sides of the equation or inequality, and using arithmetic operations to isolate the variable. The key difference is in regard to multiplication or division by negative numbers in inequalities, which leads to reversing the direction of the inequality sign.

Step 1: Identify the similarities

Both linear equations and inequalities start with a problem to be solved usually showing an equation or inequality with one variable.

Step 2: Simplify both sides

Similar to linear equations, linear inequalities are solved by simplifying both sides as much as possible. This includes combining like terms and simplifying any expressions.

Step 3: Isolate the variable

Linear equations and inequalities are solved by isolating the variable. This can be done by addition, subtraction, multiplication, or division.

Step 4: Understand the key difference

The key difference to note is that when a linear inequality is multiplied or divided by a negative number, the direction of the inequality sign flips.