What is an equation?
An equation is a math sentence that simply means two expressions are equal. It should always have an equal (=) sign. The expression that is on the left side of the equal sign is equal to the right side of the equal sign. For example:
How can equations be modeled?
If you’re a visual person, then you might like the idea of using algebra tiles, however, sometimes it’s not enough to illustrate an equation. But there’s another way you could do without algebra tiles; draw rectangles to represent x and squares as constant numbers.
Here’s how to model an equation visually w/ algebra tiles:
To solve equations visually, start by drawing out the equations:
Step 1: Sort the x first by making zero pairs
Step 2: Do the same thing on the constant numbers, but make sure to subtract them by 5 because if it’s + 4, then it will be very confusing to solve since the left side has nothing left; unequal.
The last step is to divide both sides by 4 to know how many squares will there be in one rectangle(x). And write what the solution for the equation (unnecessary to divide -9 by 4 at all.)
Solving Equations Algebraically
For this same equation, the steps are similar to what I did above; sort/zero pairs, divide:
2x-2x – 4 = 6x-2x + 5
-4-5 = 4x + 5-5
-9 ÷ 4 = 4x ÷ 4
x = -9/4
*Solving Fractional Equations
If there’s any fraction in an expression, start off by finding the common denominator first.
Then, take off the denominators by multiplying its LCD itself.
Now just do the same process again: sort/ zero pairs, and divide.
Divide:
The solution for the equation is x = 56/10
How To Check Your Answer
To tell if the solution to the equation is right, you can plot it on a graph or evaluate it – which is actually the best option, here’s how:
so my equation was 2x – 4 = 6x + 5 and the solution was x = -9/4 then I’m going to evaluate it
2(-9/4) – 4 = 6(-9/4) + 5
-17/2 = -17/2
Therefore, my solution was right.
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