The student will solve multi-step linear inequalities in one variable with the variable on one or both sides of the inequality symbol, including practical problems, and graph the solution on a number line.
You solve an inequality the same way you solve an equation.
The only exception to this is when multiplying or dividing by a negative number. If that happens, the inequality sign changes direction.
The solution to an equation is a single value/number. Inequalities are different: the solution is a set/group of numbers.
Example: for x > 5, any value that is greater than 5 makes the inequality true: 12, 897, 35, 8, etc.
Solve multi-step inequalities with the variable on one or both sides of the inequality symbol. This includes distributive property and/or combining like terms.
Convert between verbal (words) and algebraic (numbers & variables) forms of inequalities.
Solve practical problems (word problems) involving inequalities.
Graph the solution of an inequality on a number line.
Identify potential solutions and non-solutions for a given inequality.
Assign a value to the variable.
Enter the left side of the inequality as an expression.
Enter the right side of the inequality as an expression.
Check to see if the the values of each expression matches the inequality sign (less than, greater than, equal to).
Solving an inequality this way is a "trial & error" process. You'll need to see what works and how the value for the variable impacts the values for the equations.
See these pics for some trial & error in solving this inequality.
When you find the value that makes them equal, that is the number you use to solve the inequality.
Numbers that are greater / less than the number that makes them equal will tell you whether the variable is greater / less than the number.
You'll know whether the number can be equal because the inequality sign will tell you.
See extra credit page.