When we worked with one-step equations , many of those equations we could just look at and know the answer. In this lesson, let's look at equations which require more steps to solve.
A two-step equation will require two steps to solve, and generally they have a multiplication/division and a subtraction/addition. For example:
2x + 5 =11 \quad\quad \dfrac{1}{3}h - 3 =6 \quad\quad \dfrac {9-j}{2}=5
Let's first look at using a model to solve and then how to solve algebraically.
Algebra tiles allow us to represent an equation more visually. It is important to ensure that you are keeping the two sides of the equation balanced, so what you do to one side, you must do to the other.
This applet represents the equation 3x+ 1=7.
You can click and drag algebraic tiles from the bottom to the gray part on the scale. Click the reset button in the top right corner to go back to 3x+ 1=7.
Take away +1 tile .
What happens when we take away +1 unit from the left side of the scale?
What can you do to keep the scale balanced after removing +1 unit from the left side of the scale?
Instead of taking away +1 tile from the left side of the scale, what tile can we add to +1 tile so we have zero pair and can cancel it out?
If we add the same amount to each side of the equation, it will remain balanced.
If we take away the same amount from each side of the equation, it will remain balanced. If we double, triple, or even quadruple the amounts on both sides of a scale, the scale will stay balanced. In fact, we can keep it balanced by multiplying or dividing the amounts by any nonzero number - so long as it's the same on both sides.
Consider the following algebra tiles:
What should we add to the left side and right side of the equation to keep only the x tiles on the left side of the equation?
Draw the final number of algebraic tiles and write the equation to solve for x.
Find the value of x.
Algebra tiles allow us to represent an equation visually. It is important to ensure that we are keeping the two sides of the equation balanced, so what we do to one side, we must do to the other.
If we don't have algebra tiles available or if we have an equation involving fractions, then solving purely algebraically is also an option.
Remember from when we solved one-step equations:
Solve the following equation: 8m+9=65
Solve the following equation: \dfrac{x}{-9} + 10 = -5
When solving one-step equations: