Solving Inequalities Step 1: Isolate the constant term on the left side of the inequality by \( \begin{array}{l}\text { Solity: } 4.2 x+5.6<7.2-8.3 x \\ \text { the inequality. }\end{array} \quad 4.2 x+5.6<7.2-8.3 x \) both sides of

To solve the inequality \(4.2x + 5.6 < 7.2 - 8.3x\), start by moving all terms related to \(x\) to one side. This can be done by adding \(8.3x\) to both sides: \[4.2x + 8.3x + 5.6 < 7.2\] This simplifies to: \[12.5x + 5.6 < 7.2\] Next, isolate the \(x\) terms further by subtracting \(5.6\) from both sides to get: \[12.5x < 1.6\] Finally, divide both sides by \(12.5\) to find: \[x < 0.128\] Now you have the solution to the inequality! Understanding inequalities isn't just crucial for math tests! They pop up in real life scenarios like budgeting or deciding how many items you can buy without exceeding your cash limit. For instance, if you have a budget of $50 and each item costs $10, you'd formulate an inequality to solve the problem: \(10x \leq 50\), where \(x\) represents the number of items. One common mistake when solving inequalities is forgetting to flip the inequality sign when multiplying or dividing by a negative number. For example, if you had to solve \(-2x < 6\), dividing by -2 would require you to flip the sign to \(x > -3\). Always remember that little detail!