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Solving equations is crucial in prealgebra and forms the foundation for more advanced math topics. In this context, an equation is a mathematical statement indicating that two expressions are equivalent. The original problem "5 times an unknown number is 20" translates to the equation: \( 5x = 20 \). This equation tells us that when 5 is multiplied by some number (represented by \( x \)), the result is 20. By recognizing patterns in language and numbers, we turn word problems into math problems. Moreover, solving these equations requires understanding both sides need to balance, meaning any operation carried out on one side must also be performed on the other to maintain equality.

Isolating the variable means getting the variable by itself on one side of the equation. This process is crucial and often the first step in solving algebraic equations. For the equation \( 5x = 20 \), we need to manipulate the equation to solve for \( x \). Currently, \( x \) is being multiplied by 5. To isolate \( x \), we do the inverse operation of multiplication, which is division.

• Divide both sides by 5: \( x = \frac{20}{5} \).
• Perform the division to find \( x = 4 \).

By dividing both sides of the equation by the same number, we preserve the balance of the equation while simplifying to find the value of the variable \( x \). This technique is a valuable tool in solving many types of algebraic equations.

Basic arithmetic consists of four fundamental operations: addition, subtraction, multiplication, and division. These operations are essential for solving equations like \( 5x = 20 \). In this example, basic division is used to isolate the variable.

• Start with the equation \( 5x = 20 \).
• Recognize that you need to divide both sides by 5 to solve for \( x \).
• Calculate \( \frac{20}{5} \), which simplifies to 4.

Understanding how to perform these operations quickly and accurately is key in prealgebra. It allows for solving problems efficiently and understanding the relationships between numbers. Arithmetic is particularly important as it builds the base for all math calculations involved in algebraic manipulations and beyond.