Question

linear inequalities (level 1)
score: 2/5 penalty: 1 off
question
solve the following inequality for r. write your answer in simplest form.
-10r - 3 ≥ 10r + 6

Explanation:

Step1: Add 10r to both sides

To isolate the variable terms, we add \(10r\) to each side of the inequality \(-10r - 3 \geq 10r + 6\). This gives \(-10r + 10r - 3 \geq 10r + 10r + 6\), which simplifies to \(-3 \geq 20r + 6\).

Step2: Subtract 6 from both sides

Next, we subtract 6 from both sides to get the constant terms on one side. So, \(-3 - 6 \geq 20r + 6 - 6\), which simplifies to \(-9 \geq 20r\).

Step3: Divide by 20

Now, we divide both sides by 20 to solve for \(r\). Remember, since we are dividing by a positive number, the inequality sign remains the same. So, \(\frac{-9}{20} \geq r\), or \(r \leq -\frac{9}{20}\).

Answer:

\(r \leq -\dfrac{9}{20}\)