Problem 96 - Introductory Algebra for College Students

Question

Will help you prepare for the material covered in the next section. Is 6 a solution of \(4 y-7 \geq 5 ?\)

Step-by-Step Solution

Answer

Yes, 6 is a solution for the inequality \(4y - 7 \geq 5\).

Step 1: Substitute the Given Value into the Inequality

We will substitute \( y \) with 6 into the inequality. So, the inequality now becomes \(4*6 - 7 \geq 5 \)

Step 2: Perform Multiplication and Subtraction

We now simplify this by first multiplying \(4*6\) to give \(24\), and then subtract 7 from this to get our new inequality, \(24 - 7 \geq 5\). This simplifies to \(17 \geq 5\).

Step 3: Verify the Inequality

Finally, we need to check if the result of our inequality is true. Here, \(17\) is indeed greater than or equal to \(5\), therefore, yes, \(6\) is a solution of the given inequality.