Pregunta
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The solution is \( w \leq 15 \).
Solución
We're given the inequality (2/3)w – 3 ≤ 7.
Step 1. Add 3 to both sides:
(2/3)w – 3 + 3 ≤ 7 + 3
(2/3)w ≤ 10
Step 2. Multiply both sides by the reciprocal of 2/3, which is 3/2 (this step keeps the inequality direction the same since 3/2 is positive):
(3/2) · (2/3)w ≤ 10 · (3/2)
w ≤ 15
Thus, the solution is:
w ≤ 15
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Simplifique esta solución Extra Insights
To solve the inequality \( \frac{2}{3} w - 3 \leq 7 \), you first add 3 to both sides, giving you \( \frac{2}{3} w \leq 10 \). Next, multiply both sides by \( \frac{3}{2} \) to isolate \( w \), resulting in \( w \leq 15 \). Thus, \( w \) can take any value less than or equal to 15. Always remember to flip the inequality sign only when multiplying or dividing by a negative number! A common mistake is forgetting this rule when working with inequalities, leading to incorrect solutions. When in doubt, check your work by plugging values back into the original inequality!
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