Question - Solving Inequalities with Variable Isolation
Solution:
To solve the inequality $$5g + 3 \leq 37$$, we need to isolate the variable $$g$$. Here are the steps:1. Subtract 3 from both sides:\[5g + 3 - 3 \leq 37 - 3\]\[5g \leq 34\]2. Divide both sides by 5:\[\frac{5g}{5} \leq \frac{34}{5}\]\[g \leq \frac{34}{5}\]\[g \leq 6.8\]Now, let's look at the answer choices to find which ones are less than or equal to 6.8:- $$g = -8$$ is less than 6.8; hence it's a valid solution.- $$g = -5$$ is less than 6.8; hence it's a valid solution.- $$g = -2$$ is less than 6.8; hence it's a valid solution.- $$g = -1$$ is less than 6.8; hence it's a valid solution.All of the given choices $$g = -8, g = -5, g = -2, g = -1$$ are solutions to the inequality $$5g + 3 \leq 37$$.
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