To find the solution set for the equations \(3x - 2 = 7\) and the inequality \(4x + 5 \leq 21\), we will solve each one separately.
-
Solve \(3x - 2 = 7\): \[ 3x - 2 = 7 \] Add 2 to both sides: \[ 3x = 9 \] Divide by 3: \[ x = 3 \]
-
Solve \(4x + 5 \leq 21\): \[ 4x + 5 \leq 21 \] Subtract 5 from both sides: \[ 4x \leq 16 \] Divide by 4: \[ x \leq 4 \]
Now we combine the results from the two equations:
- The first one gives a single solution \(x = 3\).
- The second one provides a range of solutions \(x \leq 4\).
Therefore, the intersection of these two solutions consists of all values from the inequality that include the value from the equation. Hence, the solution set is:
\[ { x | x = 3 } \quad \text{and} \quad { x | x \leq 4 } \]
Since \(x = 3\) is included in the inequality \(x \leq 4\), the answer that represents the combined solution set is:
\[ {x | x \geq 3} \]
Thus, the correct response is:
{x | x ≥ 3} (start set x such that x is greater than or equal to 3 end set)