Problem 52 - Prealgebra

Question

Find the value of each of the following expressions when \(x = 5\). $$-7+2 x$$

Step-by-Step Solution

Answer

The value of the expression is 3.

Step 1: Substitute the Value of x

To find the value of the expression \(-7 + 2x\) when \(x = 5\), you first need to substitute \(5\) in place of \(x\) in the expression.

Step 2: Calculate 2x

After substituting, the expression becomes \(-7 + 2(5)\). Calculate \(2 imes 5\), which equals \(10\).

Step 3: Simplify the Expression

Now, you have \(-7 + 10\). Simplify this expression by performing the addition: \(-7 + 10 = 3\).

Key Concepts

Substitution Method

When working with algebraic expressions, the substitution method is a crucial step. It involves replacing variables in an equation with specific values to evaluate the expression.
In the case of the given exercise where the expression is \(-7 + 2x\), and you're asked to find the value when \(x = 5\), the substitution method comes into play by replacing \(x\) with \(5\). This transforms the expression into \(-7 + 2(5)\).
Using the substitution method helps simplify and solve otherwise complex expressions by making them more straightforward and relatable to basic arithmetic operations.

• This makes it easier to evaluate the expression using known values.
• It is particularly useful when dealing with more complex equations with multiple variables.

Simplifying Expressions

Simplifying expressions is an essential algebraic skill. It involves breaking down complex expressions into simpler forms that are easier to understand and work with.
Let’s take the expression \(-7 + 2(5)\) as an example. The substitution has been done, and now it's time to simplify.
The key steps in simplifying involve:

• Performing any multiplication or division first. In our case, \(2 \times 5 = 10\).
• Breaking down the expression further by performing any addition or subtraction. This leads to \(-7 + 10\).

By simplifying, you streamline the expression, making it easier to calculate and understand. It's important to follow the order of operations and manage any brackets or additional operations accordingly.

Basic Arithmetic Operations

Basic arithmetic operations form the foundation of more advanced mathematical concepts. They include addition, subtraction, multiplication, and division.
In solving the given expression, \(-7 + 2x\), once the value of \(x\) was substituted, basic arithmetic operations were used twice:

• First with multiplication — \(2 \times 5 = 10\).
• Followed by addition — \(-7 + 10 = 3\).

Understanding these operations and their sequence (like performing multiplication before addition) is key. They help evaluate expressions accurately. Mastery of these operations not only helps with algebra but also builds the skills needed for tackling more complex mathematical problems in the future.
By practicing these operations, you develop a strong number sense that will serve you in different areas of math.