Question
Real Tutor Solution
Tutor-Verified Answer
Answer
The solution is all real numbers \( x \) such that \( -3 \leq x < 1 \).
Solution
To solve the system of inequalities:
1. \( -x + 4 > 3 \)
2. \( -2x + 3 \leq 9 \)
**Step 1: Solve the first inequality**
\[
-x + 4 > 3
\]
Subtract 4 from both sides:
\[
-x > 3 - 4 \\
-x > -1
\]
Multiply both sides by **-1** (remember to reverse the inequality sign when multiplying or dividing by a negative number):
\[
x < 1
\]
**Step 2: Solve the second inequality**
\[
-2x + 3 \leq 9
\]
Subtract 3 from both sides:
\[
-2x \leq 9 - 3 \\
-2x \leq 6
\]
Divide both sides by **-2** (again, reverse the inequality sign):
\[
x \geq -3
\]
**Step 3: Combine the solutions**
The solutions from both inequalities must be true simultaneously. Therefore:
\[
-3 \leq x < 1
\]
**Final Answer:**
All real numbers x with –3 at most and below 1. In other words, –3 ≤ x < 1.
Reviewed and approved by the UpStudy tutoring team
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Explain 
Simplify this solution Mind Expander
To solve the first inequality \( -x + 4 > 3 \), we can start by isolating \( x \). Subtracting 4 from both sides gives us \( -x > -1 \). Multiplying both sides by -1 (and remembering to flip the inequality sign) results in \( x < 1 \). Now, for the second inequality \( -2x + 3 \leq 9 \), we again isolate \( x \). First, we can subtract 3 from both sides to get \( -2x \leq 6 \). Dividing by -2 (and flipping the inequality sign) gives us \( x \geq -3 \). Combining these results, we have \( -3 \leq x < 1 \). Thus, the solution set includes all \( x \) values within that range. In interval notation, the solution is expressed as \( [-3, 1) \).
