Solving Inequalities with Variable Isolation
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 \(5g + 3 \leq 37\).
