Problem 12 - Beginning and Intermediate Algebra

Question

Evaluate each expression for ( \(\boldsymbol{a}\) ) \(x=4\) and \((\boldsymbol{b}) x=6\). \(6 x\)

Step-by-Step Solution

Answer

For x = 4, 6x = 24. For x = 6, 6x = 36.

Step 1: Identify the Expression

The given expression is 6x. We need to evaluate it for different values of x.

Step 2: Substitute the First Value

For part (a), substitute x = 4 into the expression. ewline 6x = 6(4)

Step 3: Simplify the Expression

Calculate the multiplication: ewline 6(4) = 24

Step 4: Provide the First Result

The value of 6x for x = 4 is 24.

Step 5: Substitute the Second Value

For part (b), substitute x = 6 into the expression. ewline 6x = 6(6)

Step 6: Simplify the Expression Again

Calculate the multiplication: ewline 6(6) = 36

Step 7: Provide the Second Result

The value of 6x for x = 6 is 36.

Key Concepts

Substitution

Substitution is the process of replacing a variable in an expression with a given value. It involves identifying which variable needs to be replaced and then inserting the specified number in its place.

This is an essential step in evaluating algebraic expressions. For example, to evaluate the expression 6x when x = 4, we substitute 4 for x:
\[ 6x = 6(4) \]
This action simplifies the expression and prepares it for further operations, such as multiplication.

Multiplication

After substitution, the next step is multiplication. This process involves multiplying the number that replaces the variable by the coefficient of the variable.

Using the same example where x = 4, we have substituted 4 into the expression 6x to get 6(4). The multiplication step is then:
\[ 6(4) = 24 \]
Multiplication is straightforward but requires careful calculation to avoid mistakes.

Simplification

Simplification is the final step, where we combine like terms and perform all arithmetic operations to get the simplest form of the expression.

Once multiplication is done, the expression is already simplified if there are no more operations left. For example, in our case with the expression 6(4), after calculating the multiplication, we get 24.

This is the simplest form and hence, our final result for the expression 6x at x = 4 is:
\[ 24 \]
Similarly, when x = 6, the process would be:
\[ 6x = 6(6) = 36 \]
Again, 36 is the simplified form and the final result.