Question
2. Solve for \( y \) : \[ \frac{y+3}{2}+5>8 \]
Ask by Ayala Ayala. in South Africa
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( y > 3 \)
Solution
Solve the equation \( \frac{y+3}{2}+5>8 \).
Solve the inequality by following steps:
- step0: Solve for \(y\):
\(\frac{y+3}{2}+5>8\)
- step1: Multiply both sides:
\(\left(\frac{y+3}{2}+5\right)\times 2>8\times 2\)
- step2: Multiply the terms:
\(y+3+10>16\)
- step3: Simplify:
\(y+13>16\)
- step4: Move the constant to the right side:
\(y>16-13\)
- step5: Subtract the numbers:
\(y>3\)
The solution to the inequality \( \frac{y+3}{2}+5>8 \) is \( y > 3 \).
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Simplify this solution The Deep Dive
To solve the inequality \(\frac{y+3}{2} + 5 > 8\), start by isolating the fraction. Subtract 5 from both sides: \[ \frac{y+3}{2} > 3. \] Now, multiply both sides by 2 to eliminate the denominator (remember, multiplying by a positive number doesn't change the inequality direction): \[ y + 3 > 6. \] Next, subtract 3 from both sides to solve for \(y\): \[ y > 3. \] So, the solution to the inequality is \(y > 3\).
