Give an example if a LINEAR EQUATION.

Question

A LINEAR EQUATION has an equal sign (in order to be an equation in the first place), and the unknown is raised to the first power and no higher power (that is, the exponent is 1).

Example: 3x - 4 = 5x + 18

Answer 1

Our objective when we say 'Solve the equation' is to find out what number we can stick in for x to make both sides end up the same. AN ESSENTIAL IDEA TO FOLLOW IS THAT WHAT WE DO TO ONE SIDE OF THE EQUATION WE ALSO HAVE TO DO TO THE OTHER SIDE! We want to get all the x's on one side and all the not-x's on the other side.

We can start by adding 4 to each side. 3x - 4 + 4 = 5x + 18 + 4 which simplifies to 3x = 5x + 22.

We can subtract 5x from both sides to get the x's alone on one side. 3x - 5x = 5x + 22 - 5x

and this simplifies to -2x =22.

Now, to get x alone, we'll divide both sides by -2. (-2x)/-2 = 22/-2 which tells us that x = -11

If we go back to the original equation and replace x with -11, we can check to see that both sides come out the same. 3(-11) - 4 does that equal 5(-11) +18? On the left, we get -33 - 4 which equals -37; and on the right we get -55 +18 which also equals -37.

If all this raises questions in your mind as to 'why we did this' or 'why we did not do that,' know that there are many ways to solve these equations (and when you get really good at this, you'll probably do more than one step at a time) AND know that there are many things we learned before coming to this equation - things like addition and subtraction of negatives and positives, the Associative Property of Addition, the Commutative Property of Addition, what 'like terms' are, and so on. Again if all this seems confusing, give me a chance to explain and let me get you started where YOU need to start!