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Chapter 1: Problem 113

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

Short Answer

Expert verified
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 by step solution

01

Identify the similarities

Both linear equations and inequalities start with a problem to be solved usually showing an equation or inequality with one variable.
02

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.
03

Isolate the variable

Linear equations and inequalities are solved by isolating the variable. This can be done by addition, subtraction, multiplication, or division.
04

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.

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Most popular questions from this chapter

In Exercises \(1-8,\) add or subtract as indicated and write the result in standard form. $$6-(-5+4 i)-(-13-11 i)$$

Solve each quadratic inequality in Exercises \(1-28\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ x^{2}-4 x \geq 0 $$

In Exercises \(9-20,\) find each product and write the result in standard form. $$(2+3 i)^{2}$$

In Exercises \(29-44,\) perform the indicated operations and write the result in standard form. $$5 \sqrt{-16}+3 \sqrt{-81}$$

In Exercises \(1-16,\) solve and check each linear equation. $$ 7 x-5=72 $$
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