Questions: -4(x+5)+33 ≤ 4(3-x)

Transcript text: $-4(x+5)+33 \leq 4(3-x)$

Solution

Solution Steps

To solve the inequality $-4(x+5)+33 \leq 4(3-x)$, we will first expand both sides of the inequality. Then, we will combine like terms and isolate the variable $x$ on one side to find the solution set. Finally, we will determine if the solution is a specific range of $x$ values or if all real numbers are solutions.

Step 1: Expand and Rearrange the Inequality

We start with the inequality: \[ -4(x+5) + 33 \leq 4(3-x) \] Expanding both sides gives: \[ -4x - 20 + 33 \leq 12 - 4x \] This simplifies to: \[ 13 - 4x \leq 12 - 4x \]

Step 2: Analyze the Inequality

Next, we observe that the terms $-4x$ on both sides cancel out, leading to: \[ 13 \leq 12 \] This statement is false, indicating that there are no values of $x$ that satisfy the original inequality.

Step 3: Conclusion

Since the inequality leads to a false statement, we conclude that there are no solutions for $x$.