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Cross multiplication is a useful technique for solving equations involving fractions. It is particularly effective when you have two ratios or fractions set equal to each other, like in our exercise: \(\frac{5}{n+1}=\frac{7}{3}\). To cross multiply, multiply the numerator of the first fraction by the denominator of the second fraction, and the numerator of the second fraction by the denominator of the first fraction.
This process eliminates the fractions by creating a single equation without denominators.
In this example, you perform the following operations:

• Multiply 5 by 3.
• Multiply 7 by \(n+1\).

After cross multiplication, you'll get the equation \(5 \times 3 = 7 \times (n+1)\). This crucial step simplifies into an equation that is easier to solve.

Simplifying equations involves breaking down complex equations into more manageable forms. In our example, after cross multiplication, the equation becomes \(15 = 7(n+1)\).
First, distribute 7 on the right side of the equation to both terms inside the parentheses, resulting in the expression \(15 = 7n + 7\).
This step involves basic distributive property, which states that \(a(b + c) = ab + ac\).
It's simpler to work with equations once they're fully expanded and terms are isolated, as it prepares the equation for further solving steps.
Always aim to make equations as straightforward as possible to ease solving them later.

Solving for a variable means isolating the variable on one side of the equation to find its value. In this case, after simplifying to the equation \(15 = 7n + 7\), you'll work on getting \(n\) alone on one side of the equation.
First, subtract 7 from both sides to remove the constant term from the side with the variable. This yields \(8 = 7n\).
Next, divide both sides by 7 to solve for \(n\), giving \(n = \frac{8}{7}\).
When solving, remember to perform the same operation on both sides of the equation to maintain balance.
This process helps in finding the exact value of the unknown variable. By maintaining consistent steps such as adding, subtracting, multiplying, or dividing evenly across both sides, you ensure the equation remains equivalent through each modification.