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Chapter 1: Problem 82

Evaluate each expression for \(x=6, y=-4,\) and \(a=3\) $$ 6 x-5 y+4 a $$

Short Answer

Expert verified
The value of the expression is 68.

Step by step solution

01

Identify the values of the variables

Assign the given values to the variables: \( x = 6 \), \( y = -4 \), and \( a = 3 \).
02

Substitute the values into the expression

Replace \( x \), \( y \), and \( a \) with their respective values in the expression \( 6x - 5y + 4a \). \[ 6(6) - 5(-4) + 4(3) \]
03

Perform the multiplications

Multiply the constants by the variable values: \[ 6(6) = 36, \] \[ 5(-4) = -20, \] \[ 4(3) = 12. \]
04

Simplify the expression

Substitute the results of the multiplications back into the expression and then perform the addition and subtraction: \[ 36 - (-20) + 12 \] Recall that subtracting a negative number is the same as adding the absolute value: \[ 36 + 20 + 12 \]
05

Calculate the final result

Add the numbers together to get the final result: \[ 36 + 20 + 12 = 68 \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

substitution of variables
Substitution of variables is an essential concept in algebra. It involves replacing the variables in an expression with their given values. For instance, in the exercise, the variables provided were:
  • x = 6
  • y = -4
  • a = 3
To substitute these into the expression \(6x - 5y + 4a\), replace each variable with its respective value, leading to: 6(6) - 5(-4) + 4(3). This step ensures we transform the algebraic expression into arithmetic, making computations straightforward.
multiplication of constants
Once the variables have been substituted, the next step involves performing the multiplications. Each term in the expression needs to be multiplied by its coefficient:
  • For the first term, 6 is multiplied by 6, resulting in 36.
  • For the second term, -5 is multiplied by -4, resulting in 20 (since the product of two negative numbers is positive).
  • For the third term, 4 is multiplied by 3, resulting in 12.
So, our expression after multiplication is: \(36 + 20 + 12\), making it much simpler to handle.
simplification of expressions
Simplifying expressions is the final and crucial step in evaluating an algebraic expression. Once the multiplication is done, sum up the results: First, rewrite the expression with the results of the multiplications: \(36 + 20 + 12\).Then, proceed to perform the arithmetic operations: 36 + 20 = 56 馃挕 (adding 36 and 20). Next, add the last result: 56 + 12 = 68. Thus, the simplified and final result of the expression is 68. Simplifying ensures the expression is presented in its simplest form, making the answer clear and understandable.

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Most popular questions from this chapter

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