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Evaluating a Variable Expression

Evaluate the expression [tex]-0.4(3x - 2) + \frac{2x + 4}{3}[/tex] for [tex]x = 4[/tex].

[tex]\(\boxed{\phantom{}} \)[/tex]


Sagot :

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].
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