Sure! Let's evaluate the expression [tex]\(-0.4(3x - 2) + \frac{2x + 4}{3}\)[/tex] step-by-step for [tex]\(x = 4\)[/tex].
1. Substitute [tex]\(x = 4\)[/tex] into the expression:
[tex]\[
-0.4(3(4) - 2) + \frac{2(4) + 4}{3}
\][/tex]
2. Evaluate the first part of the expression, [tex]\(-0.4(3(4) - 2)\)[/tex]:
[tex]\[
3(4) = 12
\][/tex]
So the expression becomes:
[tex]\[
-0.4(12 - 2)
\][/tex]
Calculate inside the parentheses:
[tex]\[
12 - 2 = 10
\][/tex]
Now multiply by -0.4:
[tex]\[
-0.4 \times 10 = -4.0
\][/tex]
3. Evaluate the second part of the expression, [tex]\(\frac{2(4) + 4}{3}\)[/tex]:
[tex]\[
2(4) = 8
\][/tex]
So the expression becomes:
[tex]\[
\frac{8 + 4}{3}
\][/tex]
Calculate inside the parentheses:
[tex]\[
8 + 4 = 12
\][/tex]
Now divide by 3:
[tex]\[
\frac{12}{3} = 4.0
\][/tex]
4. Combine the results from steps 2 and 3:
[tex]\[
-4.0 + 4.0
\][/tex]
5. Perform the final addition:
[tex]\[
-4.0 + 4.0 = 0.0
\][/tex]
So, the value of the expression [tex]\(-0.4(3x - 2) + \frac{2x + 4}{3}\)[/tex] when [tex]\(x=4\)[/tex] is [tex]\(0.0\)[/tex].
