Problem 461 In the following exercises, eval... [FREE SOLUTION]

91影视

Prealgebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2016 Edition

Chapter 3: Problem 461

In the following exercises, evaluate each expression. $$ 7 x-3 \text { when } x=-9 $$

Short Answer

Expert verified

The value of the expression is -66.

Step by step solution

- Substitute the Given Value

Insert the given value of the variable into the expression. In this case, substitute $x = -9$ into $7x - 3$. The expression becomes: \[7(-9) - 3\].

- Perform the Multiplication

Calculate the product of the constants and the variable. Multiply 7 by -9: \[7 \times -9 = -63\]. The expression now is: \[-63 - 3\].

- Complete the Subtraction

Perform the subtraction with the result from the previous step. Subtract 3 from -63: \[-63 - 3 = -66\].

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Key Concepts

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

Variable Substitution

When solving algebraic expressions, the first step is often to substitute a given value for a variable. This is called variable substitution. In the exercise $7x - 3$ when $x = -9$, we replace $x$ with $-9$. The expression becomes $7(-9) - 3$.

Variable substitution is helpful because it lets you simplify expressions by turning variables into specific numbers. This makes it possible to focus on basic arithmetic operations like multiplication and subtraction.

Multiplication

Once you've substituted the variable with its given value, the next step is to perform any multiplications in the expression. In our example, we need to multiply 7 by -9. This gives us: $7 \times -9 = -63$.

Here are a few helpful tips on multiplication:

Positive times positive equals positive ($+ \times + = +$)
Positive times negative equals negative ($+ \times - = -$)
Negative times negative equals positive ($- \times - = +$)

In this case, we multiplied a positive number (7) by a negative number (-9), resulting in a negative product (-63).

Subtraction

Finally, after performing the multiplication, we are left with a simpler expression that involves subtraction. In our exercise, we now have: $-63 - 3$.

To complete the subtraction, just follow the same rules as basic arithmetic. Since both numbers are negative and we are subtracting, it鈥檚 like adding the absolute values and keeping the negative sign: $-63 - 3 = -66$.

Here are some pointers for dealing with subtraction:

Subtracting a positive number increases the negativity of a negative result ($-a - b = -(a + b)$)
Subtracting a negative number is like adding ($-a - (-b) = -a + b$)

In our example, since -63 is already negative, subtracting 3 makes it even more negative.

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91影视

In the following exercises, evaluate each expression. $$ 7 x-3 \text { when } x=-9 $$

Short Answer

Step by step solution

- Substitute the Given Value

- Perform the Multiplication

- Complete the Subtraction

Key Concepts

Variable Substitution

Multiplication

Subtraction

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