Make the given changes in the indicated examples of this...

Make the given changes in the indicated examples of this section and then perform the indicated operations.
In Example 4, change the $1 / 4$ to $7 / 4$ and then solve and display the resulting inequality. $\quad x $ $\quad x<-\frac{1}{2}$\quad x<-\frac{1}{2}$-\frac{1}{2}$

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Key Concepts

Linear Inequalities

This concept involves expressions that relate two quantities with inequality symbols such as <, >, ?, or ?. Solving linear inequalities requires isolating the variable on one side of the inequality, often using operations like addition, subtraction, multiplication, or division. Special rules, such as reversing the inequality sign when multiplying or dividing by a negative number, are key parts of the process.

Fraction Arithmetic

Fraction arithmetic is the process of performing operations such as addition, subtraction, multiplication, or division on fractions. When an inequality or equation involves fractions, it is essential to properly manipulate these elements, which might include finding a common denominator or simplifying the fractions to ensure accurate results through the algebraic manipulations.

Algebraic Manipulation

Algebraic manipulation refers to the techniques used to rearrange and simplify mathematical expressions to isolate the variable of interest. This includes combining like terms, handling fractional coefficients, and logically applying arithmetic operations to maintain equality or inequality. Mastery of these techniques is crucial for modifying and solving equations or inequalities after any changes have been made to their components.

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