Sure, let's evaluate the expression [tex]\(-0.4(3x - 2) + \frac{2x + 4}{3}\)[/tex] for [tex]\(x = 4\)[/tex]. Follow these steps to find the result:
Step 1: Substitute [tex]\(x = 4\)[/tex] into the expression.
[tex]\[
-0.4(3(4) - 2) + \frac{2(4) + 4}{3}
\][/tex]
Step 2: Simplify the terms inside the parentheses and fraction.
First, evaluate the term inside the first set of parentheses:
[tex]\[
3(4) - 2 = 12 - 2 = 10
\][/tex]
So, the expression becomes:
[tex]\[
-0.4(10) + \frac{2(4) + 4}{3}
\][/tex]
Next, evaluate the term inside the fraction:
[tex]\[
2(4) + 4 = 8 + 4 = 12
\][/tex]
So, the expression now looks like:
[tex]\[
-0.4(10) + \frac{12}{3}
\][/tex]
Step 3: Evaluate the simplified terms.
First, calculate [tex]\(-0.4 \times 10\)[/tex]:
[tex]\[
-0.4 \times 10 = -4.0
\][/tex]
Next, calculate [tex]\(\frac{12}{3}\)[/tex]:
[tex]\[
\frac{12}{3} = 4
\][/tex]
Step 4: Combine the results from Step 3.
[tex]\[
-4.0 + 4
\][/tex]
Step 5: Add the two values together.
[tex]\[
-4.0 + 4 = 0.0
\][/tex]
Therefore, after evaluating the expression [tex]\(-0.4(3x - 2) + \frac{2x + 4}{3}\)[/tex] for [tex]\(x = 4\)[/tex], we get the result of [tex]\(0.0\)[/tex].
To summarize, the individual parts were:
[tex]\[
-0.4(3x - 2) = -4.0
\][/tex]
[tex]\[
\frac{2x + 4}{3} = 4.0
\][/tex]
And together they sum to [tex]\(0.0\)[/tex].
