we learned to form simple equations. Today, we will learn how to solve simple equation involving a single variable, also known as $Linear\ equation$.
Before we begin our examples, let us remember a few things.
- A single equation can contain a single $=$ sign.
- We can perform the same operation with the same operator on both side of the $=$ sign, except for multiplication or division by zero. The reason for this is that, since both sides of the equation have the same value, then if we add, subtract, multiply or divide both sides by the same operand, the two sides of the equation will continue to remain the same.
- The final step of the equation involved having only the variable on one side, with no other number, and on the other side we should have only number values and no unknown. That is if we have an equation like $\unicode{0x2018}x = some\ known\ terms\unicode{0x2019}$, then we know the value of $x$ by finding the value of the known side.
Now, let us get on with an example, and try to solve the equation:
$5x + 3 = 48$
Let us look at the equation as two equal values on either side of the $\unicode{x201C}=\unicode{x201D}$ sign. Now, we know that when we perform the same operation with the same operand on the same value, we always get the same result.
So, as a first step we can subtract 3 from both sides of our example, and we get:
$5x + 3 - 3 = 48 - 3$
$\texttip{\Rightarrow}{follows that} 5x + 0 = 45$
$\texttip{\Rightarrow}{follows that} 5x = 45$
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Now we can divide both sides of the equation by five, and we get: