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)
Responses
{b:b>3}
left brace b colon b greater than 3 right brace
{b:b<3}
left brace b colon b less than 3 right brace
{b:b>15}
left brace b colon b greater than 15 right brace
{b:b<15}
left brace b colon b less than 15 right brace
{b:b>3}
left brace b colon b greater than 3 right brace
The correct set notation that expresses the solutions of the inequality 3(b−4)+2b>3 as values of b greater than three is:
{b : b > 3}
(left brace b colon b greater than 3 right brace)
The correct set notation that expresses the solutions is {b : b > 3}. This can be read as "the set of values of b such that b is greater than 3."
To determine this, we start with the given inequality: 3(b - 4) + 2b > 3.
First, we simplify the inequality:
3b - 12 + 2b > 3.
Combining like terms:
5b - 12 > 3.
Next, we isolate the variable by adding 12 to both sides of the inequality:
5b > 15.
Finally, we divide both sides by 5 to solve for b:
b > 3.
This tells us that the solution set consists of values of b greater than 3, which can be expressed using set notation as {b : b > 3}.