Solving+Equations+Multiple+Ways

In this equation: The first step is to divide both sides by two which divides both sides into two equal groups. The second step is to subtract 2 from both sides and then subract 2x's from both sides. You do this to isolate the variables on one side and the constants on the other. We get lucky in this case that there is only one x left, but if there were more than one, we would need to divide both sides into equal groups so one x was in each group to get the solution.

The most important decision in this method is to divide both sides by 2 as the first step. Since both sides divide 'nicely' or evenly it is easier to divide both sides by two rather than use the distributive property to simplify the left side of the equation, which in the long run makes you use 4 or 5 steps to solve the equation (instead of 3).

I learned that a solution to an equation means it makes both sides give you the same answer. In this example when you substitute 4 in for x you get 28 on both sides of the equation, and that means on the graph it's the point of intersection (the point where the two sides intersect each other).

I made the equation 2x + 4 = 3x + 7 and when I graphed it on geogebra I got this graph to prove the solution was 3. The second answer confirms that 3 is the solution to the equation.