Joe Pagano

Why Study Math? - Solving Multi-Step Linear Inequalities - Part I



Posted: Tuesday, May 03, 2011

by Joe Pagano
Math by Joe

Unlike an equation, which shows balance or harmony among two expressions, an inequality shows imbalance. That is, an inequality states that one expression is bigger than or less than another expression. Linear inequalities involve expressions which are lines, or linear equations. These inequalities are solved much the same way as equations with one key difference. Read on to enter this curious world.

Let us take the linear equation 2x + 1 = 5. You know to solve for the unknown, x, you subtract 1 from both sides and then divide by 2. Thus x = 2. If we replace the "=" symbol by an inequality symbol such as "" greater than, we have a linear inequality. If we choose the former we have 2x + 1 with the = symbol to get = greater than or equal to. In these cases, the "=" symbol permits the right and left sides of the expression to be equal.)

To solve an inequality, we carry out the exact same steps as if it were an equation, keeping the inequality symbol intact. Thus in 2x + 1 = 8. In words, this inequality states that the quantity 3y - 4 is bigger than or equal to the quantity 8. Visually in terms of our balance scale, this inequality says that the left side is in balance with or bigger, that is tipping left, than the right side. To solve, we simply add 4 to both sides and then divide by 3. Doing so gives that y >= 4. Thus if we choose y to be any weight equal to or bigger than 4, our given "imbalance" or balance, in the case when both sides are equal, will be maintained.

The next time you see an expression involving one of the "imbalance" symbols, know that you have an inequality, and that to solve, really requires nothing new. There are some situations, however, that require a little more care. Those we get to in Part II.
This Article has been viewed 149 times. (Not updated in real-time.)
No comments yet.
We want your comments! If you can read this, you don't have javascript enabled, so you can't use this comment system. Please enable javascript.