Solving Multi-Step Inequalities Detailed Solution Guide

To solve an equation involving multiple operations, start by simplifying both sides as much as possible. Isolate the variable by performing inverse operations. First, remove any additions or subtractions from the equation.

Next, address multiplication or division. If the variable is multiplied by a coefficient, divide both sides by that number. If it’s divided, multiply both sides by the reciprocal to eliminate the fraction. Always maintain balance by performing the same operation on both sides.

After isolating the variable, ensure that any inequalities are properly handled. Remember that when multiplying or dividing by a negative number, the inequality sign must be reversed. This step is crucial to obtaining the correct solution.

Finally, verify your solution by substituting the value back into the original equation. Check that both sides of the equation are equal, ensuring that the solution satisfies all conditions.