Question

1. when linus is asked to solve 20 - 3x > 8, he first determines that when x = 4, 20 - 3x = 20 - 3(4) = 8. explain how linus can figure out if the solution to the inequality is x > 4 or x < 4.

Explanation:

Step1: Isolate variable terms

Subtract 20 from both sides of $20 - 3x>8$. We get $20-20 - 3x>8 - 20$, which simplifies to $-3x>-12$.

Step2: Solve for x

Divide both sides of $-3x>-12$ by - 3. When dividing an inequality by a negative number, the direction of the inequality sign changes. So $\frac{-3x}{-3}<\frac{-12}{-3}$, resulting in $x < 4$.

Answer:

The solution to the inequality $20 - 3x>8$ is $x < 4$. Linus can solve the inequality by following the steps of isolating the variable - term and then solving for $x$, while remembering to reverse the inequality sign when dividing by a negative number.