Common Core Standards: Math
3. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
With linear equations, students should be able to find the solution or solutions that make the equation true. We usually get one or several specific answers with equations, but inequalities sing a slightly different tune. As different as Under Pressure and Ice Ice Baby.
Students should first understand the difference between an equation and inequality. An equation uses the = sign while an equality may use <, >, ≤, or ≥. If we find that x ≤ 2, we know that x can be 2 or anything less than 2. If we know that x < 2, x cannot be 2, but it can be anything less than 2.
With inequalities, students should find the set of numbers that make the inequality true. Inequalities won't tell us exactly which number x will equal. Instead, it'll give us a range of possible x values, all of which will work for the inequality.
Students should also know how to work with inequalities. Algebraically, they aren't that different from an equal sign. Still, multiplying and dividing by negative numbers switches the direction of the sign (1 > -2 but multiplying both sides by -1 gives us -1 < 2).
If students are unsure, it might be helpful for them to visualize inequalities on a number line. Sometimes, letters may represent constants and coefficients in equations. Students should know how to treat these as numbers. For instance, the answer to the equation x + 4m = 2x + m would be written as x = 3m. It's okay for our solution to be in terms of m because m is treated as a constant. Isn't that nice, nice, baby?
We apologize in advance if that baseline is stuck in your head for the rest of the day.