Question

linear inequalities (level 2)
score: 1/5 penalty: 1 off
question
solve the following inequality for r. write your answer in simplest form.
-7r - 5(-6r - 3) < 8r + 3 - 3r
answer attempt 2 out of 2
r < □ submit answer

Explanation:

Step1: Expand the left - hand side

Expand $-5(-6r - 3)$ using the distributive property $a(b + c)=ab+ac$. We get $-7r+30r + 15<8r + 3-3r$.

Step2: Combine like terms on both sides

On the left - hand side, $-7r+30r=23r$, so it becomes $23r + 15$. On the right - hand side, $8r-3r = 5r$, so the inequality is $23r+15<5r + 3$.

Step3: Move the terms with $r$ to one side

Subtract $5r$ from both sides: $23r-5r+15<5r-5r + 3$, which simplifies to $18r+15<3$.

Step4: Move the constant term to the other side

Subtract 15 from both sides: $18r+15 - 15<3-15$, getting $18r<-12$.

Step5: Solve for $r$

Divide both sides by 18: $r<-\frac{12}{18}$, and simplify the fraction to $r<-\frac{2}{3}$.

Answer:

$-\frac{2}{3}$