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Chapter 3: Problem 4

Evaluate the expression at the given value of \(\mathrm{x}\). $$6 x-1\( at \)x=-10$$

Short Answer

Expert verified
The value is -61.

Step by step solution

01

Understand the Expression

We are given the expression \(6x - 1\) and we need to evaluate it for a specific value of \(x\), which is \(-10\). Evaluating this expression means substituting \(-10\) into the expression in place of \(x\).
02

Substitute the Given Value

Replace \(x\) in the expression \(6x - 1\) with \(-10\). This gives us \(6(-10) - 1\).
03

Multiply

Calculate \(6 \times (-10)\). When you multiply 6 and -10, you get \(-60\). So the expression becomes \(-60 - 1\).
04

Subtract

Now, perform the subtraction \(-60 - 1\). When you subtract 1 from -60, you get \(-61\). This is the value of the expression when \(x = -10\).

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Key Concepts

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

Substitution
Substitution in algebra involves replacing a variable with a given number or expression. This is a fundamental skill that allows you to simplify expressions and solve equations.
In the exercise above, we are asked to substitute the number \(-10\) wherever we see \(x\) in the expression \(6x - 1\).
Here鈥檚 how you do it:
  • Identify the variable: \(x\).
  • Determine the value to substitute: \(-10\).
  • Replace \(x\) with \(-10\) to form the new expression: \(6(-10) - 1\).
It鈥檚 as if you鈥檙e updating the expression with a specific value to see how it changes. This process is essential not only in algebra but also in understanding how variables function in formulas across different fields.
Multiplication of Integers
Multiplication of integers is a crucial concept in mathematics, involving the operation of multiplying whole numbers, including negatives and positives.
In the step of multiplying \(6\) by \(-10\), the rules for multiplying integers are applied. Here鈥檚 how this works:
  • When you multiply a positive integer by a negative integer, the product is negative.
  • Multiplying \(6\) (a positive number) with \(-10\) (a negative number), you get \(-60\).
Understanding these rules is important as they help in accurately carrying out calculations involving integers. Be sure to remember these when dealing with signs in multiplication, as they directly impact the result.
Order of Operations
The order of operations is a mathematical principle that determines the correct sequence of steps to carry out in a given expression. This principle ensures that everyone solves expressions in the same way and arrives at the same answer.
For the expression \(6(-10) - 1\), the order of operations guides us through:
  • First, perform multiplication (as multiplication comes before subtraction in the standard order), so we multiply \(6\) and \(-10\) to get \(-60\).
  • Then, move to subtraction, where we subtract \(1\) from \(-60\) to reach the final answer, \(-61\).
Commonly remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)), this rule helps avoid errors in complex calculations by specifying the priority of each operation.

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