Question
\( 6 m+8>-10 \) or \( 10 m+9<39 \) Solution Interval Notation \( \square \)
Ask by Nunez Marsh. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The solution interval is \((-3, 3)\).
Solution
Solve the equation \( 6m+8>-10 \).
Solve the inequality by following steps:
- step0: Solve for \(m\):
\(6m+8>-10\)
- step1: Move the constant to the right side:
\(6m>-10-8\)
- step2: Subtract the numbers:
\(6m>-18\)
- step3: Divide both sides:
\(\frac{6m}{6}>\frac{-18}{6}\)
- step4: Divide the numbers:
\(m>-3\)
Solve the equation \( 10m+9<39 \).
Solve the inequality by following steps:
- step0: Solve for \(m\):
\(10m+9<39\)
- step1: Move the constant to the right side:
\(10m<39-9\)
- step2: Subtract the numbers:
\(10m<30\)
- step3: Divide both sides:
\(\frac{10m}{10}<\frac{30}{10}\)
- step4: Divide the numbers:
\(m<3\)
The solution to the first inequality \(6m+8>-10\) is \(m>-3\).
The solution to the second inequality \(10m+9<39\) is \(m<3\).
Therefore, the solution interval notation for the given inequalities is \((-3, 3)\).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
To solve the first inequality \( 6m + 8 > -10 \), subtract 8 from both sides to get \( 6m > -18 \), and then divide by 6 to find \( m > -3 \). For the second inequality \( 10m + 9 < 39 \), subtract 9 to get \( 10m < 30 \) and divide by 10, resulting in \( m < 3 \). Therefore, combining these, the solution is \( m > -3 \) or \( m < 3 \). In interval notation, this is expressed as \( (-\infty, 3) \cup (-3, \infty) \). Keep in mind when interpreting inequalities, the 'or' signifies that \( m \) can satisfy either condition. This opens up a vast range of possible values for \( m \)! So, don't be surprised if you find yourself jumping from negative to much higher positive numbers!
