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Chapter 1: Problem 97

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

Short Answer

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Step by step solution

01

- Substitute the variables

Substitute the given values into the expression: For the expression (6-x)(5+y)(3+a), substitute 6 for x, -4 for y, and 3 for a. So we have: (6-6)(5+(-4))(3+3)
02

- Simplify inside the parentheses

Simplify the values inside each set of parentheses: (6-6) = 0, (5+(-4)) = 1, (3+3) = 6. Now the expression becomes: 0 * 1 * 6
03

- Multiply the simplified values

Multiply the results from the simplified expression: 0 * 1 * 6 = 0.

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Key Concepts

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

substitution in algebra
Substitution in algebra is the process of replacing variables in an expression with their given numerical values. This step is crucial as it allows us to transform an algebraic expression to a numerical one, making it easier to evaluate.

In our exercise, we were given specific values for the variables:
  • \( x = 6 \)
  • \( y = -4 \)
  • \( a = 3 \)
To perform substitution, simply replace each variable in the expression i.e. \((6-x)(5+y)(3+a)\) with the provided values.

So, the expression becomes:
\((6-6)(5+(-4))(3+3)\).
This step is foundational for further simplification.
simplifying algebraic expressions
After substitution, the next crucial step is simplifying each part of the expression inside the parentheses. Simplification makes the expression less complex and prepares it for the final evaluation.

Here are the steps we took to simplify:
  • We substituted 6 for x, -4 for y, and 3 for a: \((6-6)(5+(-4))(3+3)\)
  • Then, we simplified each part inside the parentheses: \((6-6) = 0\), \((5+(-4)) = 1\), and \((3+3) = 6\)

Now, the expression became:
\(0 \times 1 \times 6\).
Simplifying inside the parentheses ensures that we are dealing with the simplest form of each component before proceeding to the final multiplication.
evaluating expressions step-by-step
Evaluating expressions step-by-step involves breaking down the problem into smaller, manageable parts. This methodical approach ensures accuracy and clarity.

For our given expression, here鈥檚 how we evaluated it step-by-step:
  • First, we performed substitution: \((6-6)(5+(-4))(3+3)\)
  • Next, we simplified inside the parentheses: \( (6-6) = 0 \), \( (5 + (-4)) = 1 \), \( (3+3) = 6 \)
  • Finally, we multiplied the simplified values together: \(0 \times 1 \times 6 = 0\)

Performing each step carefully helps prevent mistakes and ensures that the final evaluated result is accurate. The final result for this exercise is 0.

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Most popular questions from this chapter

Write each sentence as an equation, using \(x\) as the variable. Then find the solution of the equation from the set of integers between -12 and \(12,\) inclusive. An integer is divisible by 12 if it is divisible by both 3 and \(4,\) and not otherwise. (a) Is 4,249,474 divisible by \(12 ?\) (b) Is 4,253,520 divisible by \(12 ?\)

Solve each problem. The surface, or rim, of a canyon is at altitude \(0 .\) On a hike down into the canyon, a party of hikers stops for a rest at \(130 \mathrm{~m}\) below the surface. The hikers then descend another \(54 \mathrm{~m}\). Write the new altitude as a signed number.

Use the distributive property to rewrite each expression. $$ -\frac{1}{3}(9 x-4) $$

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

Write a numerical expression for each phrase, and simplify the expression. The sum of 12 and \(-7,\) decreased by 14
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