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
Question content area bottom
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.)
StartFraction 2 left parenthesis x plus 3 right parenthesis Over 10 x minus 30 EndFraction
for xequals8
Question content area bottom
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
\(\frac{11}{25}\).
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
\(\frac{11}{25}\).