To find the solution set of the equations \(3x - 2 = 7\) and the inequality \(4x + 5 < 21\), we will solve each separately.
-
Solve the equation \(3x - 2 = 7\):
\[ 3x - 2 = 7 \]
First, add 2 to both sides:
\[ 3x = 7 + 2 \] \[ 3x = 9 \]
Now, divide both sides by 3:
\[ x = \frac{9}{3} = 3 \]
-
Solve the inequality \(4x + 5 < 21\):
\[ 4x + 5 < 21 \]
First, subtract 5 from both sides:
\[ 4x < 21 - 5 \] \[ 4x < 16 \]
Now, divide both sides by 4:
\[ x < \frac{16}{4} = 4 \]
-
Combine the results:
The solution set for the equation is \(x = 3\) and for the inequality, it is \(x < 4\).
Since \(3\) is less than \(4\), it satisfies the inequality.
Therefore, the solution set including both the equation and the inequality is:
\[ x = 3 \]
In conclusion, the solution set is \( { 3 } \).