Question
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Answer
\( x \leq 10 \)
Solution
Solve the equation \( 8x-4-5x \leq 21+5 \).
Solve the inequality by following steps:
- step0: Solve for \(x\):
\(8x-4-5x\leq 21+5\)
- step1: Subtract the terms:
\(3x-4\leq 26\)
- step2: Move the constant to the right side:
\(3x\leq 26+4\)
- step3: Add the numbers:
\(3x\leq 30\)
- step4: Divide both sides:
\(\frac{3x}{3}\leq \frac{30}{3}\)
- step5: Divide the numbers:
\(x\leq 10\)
The solution to the inequality \(8x-4-5x \leq 21+5\) is \(x \leq 10\).
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Simplify this solution Extra Insights
Let's simplify the inequality first! Combine like terms on the left side: \( 8x - 5x - 4 \leq 21 + 5 \) becomes \( 3x - 4 \leq 26 \). Next, add 4 to both sides to isolate the term with \( x \): \( 3x \leq 30 \). Finally, divide by 3: \( x \leq 10 \). This tells us solutions are all \( x \) values up to and including 10. To put this into practical terms, if you're using this inequality in a real-world scenario—like figuring out how many items you can buy with a limited budget—knowing that \( x \leq 10 \) means you can purchase up to 10 items without exceeding your financial limit! Keep those budget constraints in mind while shopping!
