Problem 50 - Algebra 1

Question

Evaluate the expression. \(6+\frac{x+2}{y}\) when \(x=7\) and \(y=3\)

Step-by-Step Solution

Answer

The evaluated expression is \(9\)

Step 1: Substitution

Substitute the given values \(x = 7\) and \(y = 3\) into the given equation: \(6+\frac{x+2}{y}\)

Step 2: Simplification

Simplify the equation after substitution: \(6+\frac{7+2}{3}\)

Step 3: More Simplification

Simplify the equation further: \(6 + \frac{9}{3}\)

Step 4: Division

Perform the division operation: \(6 + 3\)

Step 5: Addition

Perform the addition operation: \(9\)

Key Concepts

Substitution in Algebra

Algebra is all about finding unknown values. One useful technique is substitution. When we're given specific values for variables in an expression, we can substitute them into the expression to evaluate it. In our exercise, we are working with the expression \(6 + \frac{x+2}{y}\).

We substitute the given values \(x = 7\) and \(y = 3\) directly into the expression. This means anywhere we see \(x\) in the expression, we replace it with 7, and for \(y\), we replace it with 3.

This substitution is a critical step because it transforms a general algebraic expression into something we can calculate with ordinary numbers. It’s like changing a coded message into plain text that you can understand and solve!

Simplifying Expressions

After substituting the variables with their respective values, the next step is to simplify the expression. Simplification means making an expression easier to work with. It plays a crucial role, especially when dealing with fractions, coefficients, and multiple operations.

In our example, after substitution, the expression is \(6 + \frac{7+2}{3}\). The simplification process involves first resolving what's inside the fraction: \(7 + 2\), which results in \(9\).

We then replace \(7 + 2\) with 9 in the expression, so it becomes \(6 + \frac{9}{3}\). Each step of simplification gets you closer to the final answer, making it manageable to apply the basic arithmetic operations.

Basic Arithmetic Operations

Once the expression is fully substituted and simplified, we use basic arithmetic operations to find the final answer. These operations include addition, subtraction, multiplication, and division. Knowing their order is essential, as it influences the outcome.The expression is now \(6 + \frac{9}{3}\). Here, we first perform the division: \(\frac{9}{3}\), which simplifies to 3. This reduces our expression to \(6 + 3\).

The final operation is addition. We add 6 and 3 together to get 9. Thus, understanding these basic arithmetic steps ensures you can handle any expressions confidently!