Problem 13 - Algebra 1: Concepts and Skills

Question

Evaluate the expression for the given value of the variable. \(2(-5)(-x)\) when \(x=4\)

Step-by-Step Solution

Answer

The value of the expression \(2(-5)(-x)\) when \(x = 4\) is 40.

Step 1: Substitute \(x = 4\) into the Expression

Replace \(x\) in the expression \(2(-5)(-x)\) with the assigned value \(4\). Doing so, the expression becomes: \(2(-5)(-4)\).

Step 2: Multiply

Now, proceed to perform the multiplication. According to the rules of signs, a minus times a minus yields a plus. So, \(-5*(-4)\) becomes \(20\). Then, multiply that by 2. So, the expression becomes: \(2*20\).

Step 3: Final Simplification

Simply multiply 2 by 20 to get 40. Thus, the expression \(2(-5)(-x)\) equals 40 when \(x = 4\).

Key Concepts

Evaluating Expressions

In mathematics, evaluating an expression means finding its value after replacing variables with specific numbers. This process helps us understand how changes in the variables affect the expression as a whole. For example, let's consider the expression \(2(-5)(-x)\). To evaluate this expression when \(x = 4\), we perform several key steps:

• First, identify the variable that needs replacement—in this case, it's \(x\).
• Then, substitute the given value, \(x = 4\), into the expression, resulting in \(2(-5)(-4)\).
• Next, simplify the expression by performing the necessary multiplication.
• Finally, calculate the final numerical value of the expression.

By systematically evaluating expressions, we gain insights into how these values transform and their significance within mathematical contexts.

Substitution in Algebra

Substitution is a fundamental algebraic process where variables in an expression or equation are replaced with specific values or expressions. This technique can simplify complex problems by turning them into straightforward arithmetic operations. To apply substitution effectively:

• Identify all variables within the expression or equation.
• Decide the value or expression that each variable should take; in our example, \(x\) is substituted with 4.
• Carefully replace each variable with the determined value, ensuring accuracy in every step.
• Verify if the simplified expression or equation makes arithmetic calculations easier.

Substitution makes it possible to evaluate algebraic expressions, solve equations, and perform numerous other operations that reveal valuable insights.

Multiplication of Integers

Multiplication of integers involves adding an integer to itself a specific number of times. Understanding this process is crucial for problems involving algebra and arithmetic. When dealing with integers:

• Recall that multiplying two integers with the same sign (both positive or both negative) results in a positive product.
• Conversely, multiplying two integers with different signs (one positive, one negative) results in a negative product.
• In our example problem, multiplying \(-5\) and \(-4\) involves two negative integers, which yields \(20\) because their signs are the same.

After obtaining the product, proceed with any additional multiplication steps, such as multiplying \(20\) by \(2\) to finally arrive at \(40\). These principles help ensure accurate outcomes in mathematical operations.