Write the solution to the inequality in set-builder notation. 9t − 4 > 32
The solution to the inequality 9t - 4 > 32 in set-builder notation is {t | t > 4}.
To solve the inequality 9t - 4 > 32, we need to isolate the variable t. Here are the steps:
1. Add 4 to both sides of the inequality:
9t - 4 + 4 > 32 + 4
9t > 36
2. Divide both sides of the inequality by 9 to isolate t:
(9t) / 9 > 36 / 9
t > 4
Therefore, the solution to the inequality 9t - 4 > 32 in set-builder notation is:
t ∈ (4, ∞)
To find the solution to the inequality 9t - 4 > 32, we need to isolate the variable t.
First, we'll add 4 to both sides of the inequality to get rid of the constant term on the left side:
9t - 4 + 4 > 32 + 4
This simplifies to:
9t > 36
Next, we'll divide both sides of the inequality by 9 to solve for t:
9t/9 > 36/9
This simplifies to:
t > 4
So the solution to the inequality 9t - 4 > 32 is t > 4.
In set-builder notation, we can express this solution as:
{t | t > 4}
This notation reads as "the set of all t such that t is greater than 4." So any value of t that is greater than 4 would be included in the solution.