Solving equations is more or less what algebra is all about. In this lesson we will practice solving a variety of linear equations.
Note: Linear Equations are equations that have an unknown variable that is to the power of 1, i.e. x1 i.e. x, so an equation like 2x + 1 = 5x - 3. It must have no variables like x2.
Solve the following linear equations. Note that some answers may not be whole numbers.
A quick reminder of how to solve these questions:
The solutions in the above animation are repeated with a more detailed explanation below.
2x - 6 = 10
We will start to “speed up” our Inverse Operations as we get better at them. If you are unsure, try going through the previous lesson. However, for this first one, we will go over it again.
2x - 6 = 10
Identify what has been done to x on the left-hand side following the order of operations (BEDMAS)
1) Multiplied by 2
2) Subtracted by 6
Now, Inverse Operations tells us we do the opposite order with the opposite operation.
1) Add 6
2) Divide by 2
Add 6 to both sides (remember the Additive Properties of Equality and the Multiplicative Properties of Equality).
2x - 6 + 6 = 10 + 6
2x = 10 + 6
2x = 16
Divide both sides by 2
x = 8
Multiply by 3
x + 5 = 9
x = 4
When dealing with a larger equation, it might help to go over your Inverse Operations.
Identify what has been done to x, on the side of the equation that has x.
1) Brackets first, subtract 5
2) Multiply and Divide, the order does not matter for multiplication and division, but let us choose multiply, so, Multiply by 3
3) Divide by 6
4) Add 7
Now, we do the opposite of this order, with the opposite operations
1) Subtract 7
2) Multiply 6
3) Divide 3
4) Add 5
2) Multiply by 6,
3(x - 5) = -12
3) Divide by 3
x - 5 = -4
x - 5 + 5 = -4 + 5
x = 1
This might be a bit daunting seeing a fraction as a coefficient. However, stick to our rules; it might help to write a bracket around the -5/3 to help is see it as a coefficient multiplying our variable.
Firstly, subtract 3
We can solve this a couple ways.
We can it write this like,
Then multiply by 3
-5x = 6
Then divide by - 5
Something divided by a fraction is the same as multiplying something by the inverse (or flipped version) of that fraction i.e. 2 ÷ 1/2 = 2 x 2/1