Question
Solve the following in equality \( \frac{3 y+2}{2}-\frac{y-6}{3}>0 \)
Ask by Bolton Ramos. in South Africa
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( y > -\frac{18}{7} \)
Solution
Solve the equation \( \frac{3y+2}{2}-\frac{y-6}{3}>0 \).
Solve the inequality by following steps:
- step0: Solve for \(y\):
\(\frac{3y+2}{2}-\frac{y-6}{3}>0\)
- step1: Multiply both sides:
\(\left(\frac{3y+2}{2}-\frac{y-6}{3}\right)\times 2\times 3>0\times 2\times 3\)
- step2: Multiply the terms:
\(9y+6-2y+12>0\)
- step3: Simplify:
\(7y+18>0\)
- step4: Move the constant to the right side:
\(7y>0-18\)
- step5: Remove 0:
\(7y>-18\)
- step6: Divide both sides:
\(\frac{7y}{7}>\frac{-18}{7}\)
- step7: Divide the numbers:
\(y>-\frac{18}{7}\)
The solution to the inequality \( \frac{3y+2}{2}-\frac{y-6}{3}>0 \) is \( y > -\frac{18}{7} \).
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Simplify this solution Mind Expander
To solve the inequality \( \frac{3y + 2}{2} - \frac{y - 6}{3} > 0 \), we’ll first find a common denominator, which is 6: \[ \frac{3(3y + 2)}{6} - \frac{2(y - 6)}{6} > 0 \] Simplifying this, we get: \[ \frac{9y + 6 - 2y + 12}{6} > 0 \] Combining like terms: \[ \frac{7y + 18}{6} > 0 \] Now, we can multiply both sides by 6 (which is positive, so the direction of the inequality stays the same): \[ 7y + 18 > 0 \] Next, we isolate \( y \): \[ 7y > -18 \] Dividing by 7 gives us: \[ y > -\frac{18}{7} \] Thus, the solution to the inequality is: \[ y > -\frac{18}{7} \] This means any value of \( y \) greater than \(-\frac{18}{7}\) will satisfy the inequality!
