Question - Solving Linear Inequalities by Isolating Variables
Solution:
To solve the inequality 5q + 3 < 37, you need to isolate the variable q. Here are the steps:1. Subtract 3 from both sides:5q + 3 - 3 < 37 - 32. This simplifies to:5q < 343. Now, divide both sides by 5:5q / 5 < 34 / 54. You get:q < 6.8Now, let's look at the provided options:- $$ q = -8 $$ is less than 6.8, so it is a solution.- $$ q = -5 $$ is also less than 6.8, so it is a solution.- $$ q = -2 $$ is less than 6.8, so it is a solution.- $$ q = -1 $$ is less than 6.8, so it is also a solution.All four options are solutions to the inequality because they are all less than 6.8. However, if the question intends to ask for only one solution, they typically expect the greatest value that satisfies the inequality. Since $$ q = -1 $$ is the greatest value among the choices and still satisfies the inequality $$ q < 6.8 $$, it would be considered the best solution from the provided options.
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