# Solving an Equation Using Four Basic Operations

When you’re faced with a complex single variable equation like this one, the first thing you want to do is remove the fractions from this by multiplying both sides of the equation by the product of the two denominators.

So, we’re going to multiply the left and right sides of the equation by 3x.

33%

Question 1 of 3

Solve for x:  x - 7 = 12

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Question 1 of 3

Question 2 of 3

Solve for y:  17 = 12 + y

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Question 2 of 3

Question 3 of 3

Solve for x:  3x = 12

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Question 3 of 3

The next lesson: System of Linear Equations
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The following transcript is provided for your convenience.

So, if we multiply this side by 3x, what we get is we can cancel out this x, and what we’re left with is 3 times 3x+17-11.

If we multiply the right side of the equation by 3x, we can cancel out the 3, and what we’re left with is 10x.

So, now, we just have to solve this for x. This 3 gets distributed to each of these terms, so 3 times 3x is 9x, plus, 3 times 17 is 51, minus, 3 times 11 is 33, equals 10x.

Now, the next thing we want to do is get x all by itself on one side of the equation, so we’re going to subtract 9x from both sides, and that will cancel this out.

It’ll leave us with just x over here, and we still have the 51-33.

Now, to solve for x, all we have to do is subtract 33 from 51, and the solution to that is going to be 18.

So, that is how you solve an equation like that.

Remember: It’s very useful to know how to convert word problems and situations into algebraic equations.  When you write an equation, begin by asking yourself these questions:

Which quantities are known and constant? These will be represented in the equation with numbers.

Which quantities are unknown and changeable? These will be represented in the equation with variables.

What is the relationship between constants and variables? These will be represented in the equation with operation.

Once you identify what you know and what you want to find out, you can build an equation that will let you solve the problem.