Question

-30 + 5x is less than or equal to 4 (8x + 6)

Answer 1

To solve the inequality \(-30 + 5x \leq 4(8x + 6)\), we start by distributing on the right side:

\[
4(8x + 6) = 32x + 24
\]

Now, we can rewrite the inequality:

\[
-30 + 5x \leq 32x + 24
\]

Next, let's get all terms involving \(x\) on one side and constant terms on the other side. We can do this by subtracting \(5x\) and \(24\) from both sides:

\[
-30 - 24 \leq 32x - 5x
\]

This simplifies to:

\[
-54 \leq 27x
\]

Now, divide both sides by \(27\):

\[
-\frac{54}{27} \leq x
\]

This simplifies to:

\[
-2 \leq x
\]

or, alternatively:

\[
x \geq -2
\]

Thus, the solution to the inequality is:

\[
x \geq -2
\]