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Chapter 1: Problem 81

Evaluate each expression for \(x=6, y=-4,\) and \(a=3\) $$ 5 x-2 y+3 a $$

Short Answer

Expert verified
The value of the expression is 47.

Step by step solution

01

Substitute the values

Replace the variables in the expression with the given values: \(x=6\), \(y=-4\), and \(a=3\). The expression becomes: \(5(6) - 2(-4) + 3(3)\).
02

Multiply the coefficients

Compute the products: \(5(6) = 30\), \(-2(-4) = 8\), and \(3(3) = 9\).
03

Add the results

Combine the resulting terms: \(30 + 8 + 9 = 47\).

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Key Concepts

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

Substitution
Substitution is a key concept in algebra that involves replacing variables in an expression with specific values. This process simplifies the expression and makes it possible to evaluate the result. For example, if we have the expression: \(5x - 2y + 3a\), and we're given the values \(x=6\), \(y=-4\), and \(a=3\), we substitute these values directly into the expression. The expression then becomes \(5(6) - 2(-4) + 3(3)\). This new expression, with replaced values, is much easier to handle and sets us up perfectly for the next steps.
Arithmetic Operations
Arithmetic operations include addition, subtraction, multiplication, and division. These operations are fundamental when working with algebraic expressions. After substituting values into our expression, the next step is to perform arithmetic operations.
For \(5(6) - 2(-4) + 3(3)\), we start by multiplying each term.
  • First, calculate \(5 \times 6 = 30\).
  • Next, compute \(-2 \times -4 = 8\).
  • Finally, multiply \(3 \times 3 = 9\).

With these results, we can then proceed to add them together to get the final value.
Algebraic Expressions
Algebraic expressions consist of variables, constants, and arithmetic operations. Understanding how to manipulate these expressions is crucial in mathematics. In the example \(5x - 2y + 3a\), recognizing each component and their roles is essential.
  • Variables \(x, y, a\) represent unknown or variable values.
  • Constants (numbers like 5, -2, and 3) are fixed values that don't change.
  • Operations (addition, subtraction, multiplication) dictate how the variables and constants interact.

By substituting the known values and performing the arithmetic operations, we simplify and evaluate the expression. For our example, the final step is to combine the results from the arithmetic operations: \(30 + 8 + 9\). This yields the final evaluated expression as 47.

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Most popular questions from this chapter

Write a numerical expression for each phrase and simplify. See Examples 8 and \(9 .\) The difference between 7 and \(-14\)

Write a numerical expression for each phrase and simplify. The product of \(-\frac{2}{3}\) and \(-\frac{1}{5},\) divided by \(\frac{1}{7}\)

The top of Mt. Whitney, visible from Death Valley, has an altitude of \(14,494\) ft above sea level. The bottom of Death Valley is 282 ft below sea level. Using 0 as sea level, find the difference between these two elevations.

To find the average (mean) of numbers, we add the numbers and then divide the sum by the number of terms added. For example, to find the average of \(14,8,3,9,\) and \(1,\) we add them and then divide by 5. $$ \frac{14+8+3+9+1}{5}=\frac{35}{5}=7 \leftarrow \text { Average } $$ Find the average of each group of numbers. \(18,12,0,-4,\) and \(-10\)

To find the average (mean) of numbers, we add the numbers and then divide the sum by the number of terms added. For example, to find the average of \(14,8,3,9,\) and \(1,\) we add them and then divide by 5. $$ \frac{14+8+3+9+1}{5}=\frac{35}{5}=7 \leftarrow \text { Average } $$ Find the average of each group of numbers. $$ -17,34,9,-2 $$
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