# Solve Linear Inequalities Worksheet

## 6 problems

Solving linear inequalities involves finding the range of values for a variable that satisfies an inequality. These inequalities are expressed as linear expressions involving variables, constants, and inequality symbols (such as $$<$$, $$\leq$$, $$>$$, $$\geq$$). Solving them requires applying algebraic operations to isolate the variable on one side of the inequality sign. The solutions represent intervals on a number line or in coordinate planes, depicting all possible values that make the inequality true.

Algebra 2
Inequalities

## How Will This Worksheet on "Solve Linear Inequalities" Benefit Your Student's Learning?

• Reinforces understanding of linear inequalities and their solutions.
• Develops critical thinking and analytical skills through problem-solving.
• Enhances interpretation of inequalities on number lines or coordinate planes.
• Applies math concepts to real-world scenarios through inequality modeling.
• Promotes logical reasoning in interpreting and evaluating inequality solutions.
• Prepares students for assessments with inequality-solving components.
• Encourages self-directed learning and builds confidence in problem-solving abilities.

## How to Solve Linear Inequalities?

• Use addition, subtraction, multiplication, or division to isolate the variable on one side of the inequality.
• Simplify both sides of the inequality as much as possible (combine like terms, distribute if needed).
• If you multiply or divide both sides of the inequality by a negative number, flip the inequality sign.
• Perform the necessary arithmetic operations to isolate the variable.
• Write the solution in inequality form, interval notation, or graphically on a number line.
• Substitute the solution back into the original inequality to ensure it makes the inequality true.

## Solved Example

Q. Solve for $r$.$\newline$$6(r - 1) - 2 > 10$
Solution:
1. Distribute and Simplify: $6(r - 1) - 2 > 10$$\newline$First, distribute the $6$ across the terms inside the parentheses.$\newline$$6 \times r - 6 \times 1 - 2 > 10$$\newline$$6r - 6 - 2 > 10$
2. Combine Like Terms: $6r - 6 - 2 > 10$$\newline$Combine like terms on the left side.$\newline$$6r - 8 > 10$
3. Add to Isolate: $6r - 8 > 10$$\newline$Add $8$ to both sides to isolate the term with the variable $r$.$\newline$$6r - 8 + 8 > 10 + 8$$\newline$$6r > 18$
4. Divide to Solve: $6r > 18$$\newline$Divide both sides by $6$ to solve for $r$.$\newline$$\frac{6r}{6} > \frac{18}{6}$$\newline$$r > 3$

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