Basic Algebra
1. We are aiming to get x (or whatever letter the question uses) on the left hand side of the equals sign, by itself.
2. We solve equations by balancing: whatever we do to one side of an equation, we must do the same to the other side. So if we add 4 to the left hand side, we must add 4 to the right hand side as well. If we multiply on the left side by 2, we multiply on the right side by 2 as well.
Solve the equation:
x − 6 = 10
We need to "get rid of" the -6 on the left hand side so we are left with only x on the left hand side.
The opposite of subtracting 6 is adding 6.
If we add 6 to both sides, we will remove the -6 on the left.
x − 6 = 10
x − 6 + 6 = 10 + 6
x = 16
Solve the equation:
3x = 7
4
This time we need to do 2 steps to solve the equation. We notice there is a 4 on the bottom of the fraction. This is equivalent to dividing by 4. The opposite of dividing by 4 is multiplying by 4. So we do that first:
3x x 4 = 7 x 4
4
3x = 28
In the middle step we cancelled out the 4's, so we are left with no fraction.
Now we need to divide both sides by 3, since we have a "3x" on the left hand side of the equation.
3x = 28
x = 28
3
x = 9 1/3 or 9.333
Solve the equation:
5x − 2(x − 5) = 4x
Expanding the bracket:
5x − 2(x − 5) = 4x
5x − 2x + 10 = 4x
3x + 10 = 4x
10 = 4x - 3x
x = 10
1. We are aiming to get x (or whatever letter the question uses) on the left hand side of the equals sign, by itself.
2. We solve equations by balancing: whatever we do to one side of an equation, we must do the same to the other side. So if we add 4 to the left hand side, we must add 4 to the right hand side as well. If we multiply on the left side by 2, we multiply on the right side by 2 as well.
Solve the equation:
x − 6 = 10
We need to "get rid of" the -6 on the left hand side so we are left with only x on the left hand side.
The opposite of subtracting 6 is adding 6.
If we add 6 to both sides, we will remove the -6 on the left.
x − 6 = 10
x − 6 + 6 = 10 + 6
x = 16
Solve the equation:
3x = 7
4
This time we need to do 2 steps to solve the equation. We notice there is a 4 on the bottom of the fraction. This is equivalent to dividing by 4. The opposite of dividing by 4 is multiplying by 4. So we do that first:
3x x 4 = 7 x 4
4
3x = 28
In the middle step we cancelled out the 4's, so we are left with no fraction.
Now we need to divide both sides by 3, since we have a "3x" on the left hand side of the equation.
3x = 28
x = 28
3
x = 9 1/3 or 9.333
Solve the equation:
5x − 2(x − 5) = 4x
Expanding the bracket:
5x − 2(x − 5) = 4x
5x − 2x + 10 = 4x
3x + 10 = 4x
10 = 4x - 3x
x = 10