11/4x+9=31
3 answers
To solve the equation \( \frac{11}{4}x + 9 = 31 \), follow these steps:
Subtract 9 from both sides of the equation:
\[ \frac{11}{4}x + 9 - 9 = 31 - 9 \]
\[ \frac{11}{4}x = 22 \]
To isolate \( x \), multiply both sides by the reciprocal of \( \frac{11}{4} \), which is \( \frac{4}{11} \):
\[ x = 22 \cdot \frac{4}{11} \]
Now simplify the right-hand side:
\[ x = \frac{22 \cdot 4}{11} \]
\[ x = \frac{88}{11} \]
\[ x = 8 \]
Thus, the solution is
\[ \boxed{8} \]
Yes, let's go through the calculation step by step again to confirm the solution for \( x \) in the equation:
\[ \frac{11}{4}x + 9 = 31 \]
Subtract 9 from both sides:
\[ \frac{11}{4}x = 31 - 9 \]
\[ \frac{11}{4}x = 22 \]
Now, multiply both sides by the reciprocal of \( \frac{11}{4} \) (which is \( \frac{4}{11} \)):
\[ x = 22 \cdot \frac{4}{11} \]
Simplifying this:
\[ x = \frac{22 \times 4}{11} \]
\[ x = \frac{88}{11} \]
\[ x = 8 \]
So, the value of \( x \) is indeed positive and the confirmed solution is:
\[ \boxed{8} \]
If you have any further doubts, feel free to ask!
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