Question

Evaluate the expression for the given value of the variable.
StartFraction 2 left parenthesis x plus 3 right parenthesis Over 10 x minus 30 EndFraction
for xequals8
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Part 1
When xequals8 the expression StartFraction 2 left parenthesis x plus 3 right parenthesis Over 10 x minus 30 EndFraction
equals
  
enter your response here. ​(Type an integer or a simplified​ fraction.)

Answers

GPT-4o mini
To evaluate the expression \(\frac{2(x + 3)}{10x - 30}\) for \(x = 8\), we can substitute \(8\) into the expression.

First, substitute \(x\) with \(8\):

\[
\frac{2(8 + 3)}{10(8) - 30}
\]

Now, simplify the expression step by step:

1. Calculate \(8 + 3\):

\[
8 + 3 = 11
\]

2. Substitute \(11\) back into the expression:

\[
\frac{2(11)}{10(8) - 30}
\]

3. Now calculate \(10(8)\):

\[
10(8) = 80
\]

4. Then calculate \(80 - 30\):

\[
80 - 30 = 50
\]

5. Substitute \(80\) and \(50\) into the expression:

\[
\frac{2(11)}{50}
\]

6. Calculate \(2(11)\):

\[
2(11) = 22
\]

7. Now, the expression becomes:

\[
\frac{22}{50}
\]

8. Finally, simplify \(\frac{22}{50}\):

We can divide both the numerator and the denominator by 2:

\[
\frac{22 \div 2}{50 \div 2} = \frac{11}{25}
\]

Thus, the value of the expression when \(x = 8\) is

\[
\frac{11}{25}.
\]

So, the final answer is

\(\frac{11}{25}\).

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