Question

Solve the inequality and write your answer in interval notation.
2(20x-18)+7≥-16+7x

Answer 1

To solve the inequality \(2(20x - 18) + 7 \geq -16 + 7x\), we'll start by simplifying both sides.

1. Distribute the \(2\) on the left side:
\[
2(20x - 18) = 40x - 36
\]
So the inequality becomes:
\[
40x - 36 + 7 \geq -16 + 7x
\]

2. Combine the constant terms on the left:
\[
40x - 29 \geq -16 + 7x
\]

3. Next, we'll move all terms involving \(x\) to one side and constant terms to the other side. Subtract \(7x\) from both sides:
\[
40x - 7x - 29 \geq -16
\]
This simplifies to:
\[
33x - 29 \geq -16
\]

4. Now, add \(29\) to both sides:
\[
33x \geq -16 + 29
\]
This simplifies to:
\[
33x \geq 13
\]

5. Finally, divide both sides by \(33\):
\[
x \geq \frac{13}{33}
\]

Now, we write the solution in interval notation:
\[
\left[\frac{13}{33}, \infty\right)
\]

Thus, the solution to the inequality is:
\[
\boxed{\left[\frac{13}{33}, \infty\right)}
\]