Solve each equation. Leave your answer as a fraction if it...

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Key Concepts

Linear Equations

Linear equations involve variables raised only to the first power and are solved by isolating the variable through algebraic manipulations. Understanding them is fundamental in algebra since many problems require reducing expressions to a form where the variable stands alone.

Clearing Fractions

When solving equations that include fractional terms, it is often helpful to eliminate fractions by multiplying every term by a common denominator. This process simplifies the equation by converting all terms into whole-number coefficients, making subsequent steps more straightforward.

Combining Like Terms

This concept involves merging terms that have the same variable component to simplify an equation. It reduces complexity by condensing expressions, which is a critical step in isolating the variable and solving the equation.

Properties of Equality

These are the rules that allow for the same operation to be performed on both sides of an equation without changing its truth value. They are essential for maintaining balance in an equation during processes such as adding, subtracting, multiplying, or dividing both sides.

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