To solve the system of equations and inequalities, let's tackle each one separately.
-
Solve for \(3x - 2 = 7\): \[ 3x - 2 = 7 \] Add 2 to both sides: \[ 3x = 9 \] Divide both sides by 3: \[ x = 3 \]
-
Solve the inequality \(4x + 5 \leq 21\): \[ 4x + 5 \leq 21 \] Subtract 5 from both sides: \[ 4x \leq 16 \] Divide both sides by 4: \[ x \leq 4 \]
Now, we combine the results:
- From the first equation, we found \(x = 3\).
- From the inequality, we know \(x\) can be any value less than or equal to 4.
The value \(x = 3\) satisfies \(x \leq 4\). Therefore, we also include all values less than or equal to 4 in the solution set.
The solution to the system is contained within the constraint of the inequality \(x \leq 4\).
The solution set includes all \(x\) such that \(x \geq 3\), since we also have the equality \(x = 3\) and the values up to \(x = 4\) satisfy both conditions.
Thus, the final solution set for the inequalities and equation is:
\[ {x \mid x \geq 3} \]
The correct response is {x | x ≥ 3}.
1 answer