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Cross multiplication is a helpful technique used to solve proportions, which are equations that set two fractions equal to each other. In the given exercise, we use cross multiplication to eliminate the fractions and work with whole numbers. To perform cross multiplication:

• Multiply the numerator of the first fraction by the denominator of the second fraction.
• Then, multiply the numerator of the second fraction by the denominator of the first fraction.
• Set the two products equal to each other, forming a new equation without fractions.

For the original expression \(\frac{x+1}{5} = \frac{3}{15}\), you cross-multiply to get:\[ 15(x + 1) = 5 \times 3 \]This results in a linear equation, making it easier to solve for the unknown variable "x." Cross multiplication simplifies the problem by transforming the proportion into a simpler format.

A linear equation is an equation of the first degree, meaning it involves only the sum of constants and a linear term of one variable without any item being raised to a power greater than one. In our case, after cross multiplication, we end up with the equation:\[ 15x + 15 = 15 \]Such equations can typically be rewritten in the form \(ax + b = c\), where "a," "b," and "c" are constants. The goal with linear equations is to solve for the variable, which often involves isolating the variable on one side of the equation through various algebraic steps. To achieve this, you perform operations such as addition or subtraction to both sides, which brings us to our next concept: isolating the variable.

Solving equations involves arranging the equation to discover the value of the variable that makes the equation true. Starting with our linear equation:\[ 15x + 15 = 15 \]Here are the steps typically involved:

• First, isolate the term containing the variable by moving other terms to the opposite side of the equation. For instance, subtract 15 from both sides to get: \(15x = 0\).
• Next, simplify further by solving for the variable "x" by dividing both sides by 15, resulting in: \(x = 0\).

This process of solving equations often includes operations like addition, subtraction, multiplication, or division to both sides of the equation, maintaining an equal balance and uncovering the variable's value. Understanding these steps makes it easier to tackle more complex algebraic problems.