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 can follow these steps:

1. Distribute on the right side:
\[
4(8x + 6) = 32x + 24
\]
So the inequality becomes:
\[
-30 + 5x \leq 32x + 24
\]

2. Move all terms involving \(x\) to one side and constant terms to the other side. We can subtract \(5x\) from both sides:
\[
-30 \leq 32x - 5x + 24
\]
This simplifies to:
\[
-30 \leq 27x + 24
\]

3. Next, subtract 24 from both sides:
\[
-30 - 24 \leq 27x
\]
Which simplifies to:
\[
-54 \leq 27x
\]

4. Now divide both sides by 27:
\[
\frac{-54}{27} \leq x
\]
Simplifying \(\frac{-54}{27}\):
\[
-2 \leq x
\]

5. This can be rewritten as:
\[
x \geq -2
\]

Therefore, the solution to the inequality is:
\[
x \geq -2
\]