pdf Solving Inequalities

This worksheet provides focused practice with solving multi-step linear inequalities involving variables on both sides of the inequality. Students simplify expressions, use inverse operations, and isolate the variable while maintaining correct inequality direction. The problems emphasize algebraic reasoning rather than graphing, making this resource ideal for strengthening procedural fluency.

Students solve inequalities such as \(4x + 7 < 5x + 10\), \(3(x - 2) < 2x + 1\), and \(6(x + 2) \ge 4x + 16\). Several problems require distributing, combining like terms, and working with fractional solutions, reinforcing accuracy and attention to structure. Solutions are expressed symbolically, allowing students to focus on algebraic manipulation and interpretation.

By working through increasingly complex inequalities, this resource helps students build confidence and prepares them for graphing inequalities and solving more advanced expressions in later units.

Skills Assessed

• Solving one-variable linear inequalities
• Simplifying expressions using the distributive property
• Combining like terms
• Isolating variables in multi-step inequalities
• Interpreting symbolic solutions

Details

• Practice worksheet format
• 20 multi-step inequality problems
• Variables appear on both sides of the inequality
• Answer key included

ID# 0850