The solution set of the inequality 3(b−4)+2b>3 is the set of values of b greater than three. Which set notation correctly expresses the solutions?(1 point)

Answer 1

To solve the inequality \( 3(b - 4) + 2b > 3 \), let's first simplify it:

1. Distribute the 3: \[ 3b - 12 + 2b > 3 \]

2. Combine like terms: \[ 5b - 12 > 3 \]

3. Add 12 to both sides: \[ 5b > 15 \]

4. Finally, divide by 5: \[ b > 3 \]

Now, to express the solution in set notation, it can be represented as: \[ { b \in \mathbb{R} \mid b > 3 } \] or in interval notation as: \[ (3, \infty) \]

Both notations correctly express the solution set of the inequality \( b > 3 \).