Addition Principle

Lesson 1: Addition Principle

Thou shalt do unto one side of an equation what thou doest to the other”

Addition Principle

The addition principle states that if the same number is added to both sides of a true equation, the equation remains true.

addition principle

Example 1

7 = 7 i s a t r u e e q u a t i o n

Now if we add another number, say 3, to one side we have to add 3 to the other side also so that the equation remains true.

\begin{array}{l} 7 + 3 = 7 + 3 \\ 10 = 10 \end{array}

This also applies if we are working with variables. We can use this principle to solve an equation.

Example 2: Solve for "x" in $x - 3 = 7$

Solution:

Here we want to find a value for x that will satisfy this equation. For this purpose we will isolate x (get x by itself) by adding 3 to both sides.

\begin{matrix} x - 3 + 3 = 7 + 3 \\ x + 0 = 10 \\ x = 10 \end{matrix}

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Example 3: Solve $a + 12 = 9$

Solution:

In this example, to isolate "a" we need to subtract 12 from both sides of the equation.That is,
$\begin{matrix} a + 12 = 9 \\ a + 12 - 12 = 9 - 12 \\ a = - 3 \end{matrix}$

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This principle is not just limited to constants (numbers) but you can also add or subtract variables to both sides of an equation.

Example 4: Solve $2 v - 3 = v + 2$

Solution:

In this example we will see how to add and subtract both variables and numbers from each side of the equation in order to solve for "v".
$\begin{matrix} 2 v - 3 = v + 2 \\ 2 v - v - 3 = v - v + 2 \\ v - 3 = 2 \\ v - 3 + 3 = 2 + 3 \\ v = 5 \end{matrix}$

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Now let us take a look at some formulas that can be manipulated using the addition principle.

Example 5:

Let us assume "t" represents total number of students and "f" and "m" represent total number of female and male students respectively. If we know the values of "t" and "m" we can find the value of "f". This means we will solve the following equation for “f”

\begin{matrix} t = f + m \\ t - m = f + m - m \\ t - m = f \end{matrix}

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In Example 6 we will look at a more complex equation but just remember that the addition and subtraction principles work regardless of the complexity of the formula.

Example 6: $D W T = Δ - Δ_{l i g h t} for Δ$

Solution:

\begin{matrix} D W T + Δ_{l i g h t} = Δ - Δ_{l i g h t} + Δ_{l i g h t} \\ D W T + Δ_{l i g h t} = Δ \\ o r, \\ Δ = D W T + Δ_{l i g h t} \end{matrix}

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Now try some practice problems. Remember you can always come back to revisit this page and other lesson resources.