Question

solve the inequality. graph the solution set, and write the solution set in set - builder notation and interval notation.
-5>3(y - 7)+4
part: 0 / 3
part 1 of 3
apply the distributive property.
-5>3y - 21+4
-5>3y

3y

Explanation:

Step1: Simplify the right - hand side

First, simplify $3y - 21+4$ to $3y - 17$. So the inequality becomes $-5>3y - 17$.

Step2: Isolate the term with $y$

Add 17 to both sides of the inequality. We get $-5 + 17>3y-17 + 17$, which simplifies to $12>3y$.

Step3: Solve for $y$

Divide both sides of the inequality $12>3y$ by 3. We have $\frac{12}{3}>\frac{3y}{3}$, so $4>y$ or $y < 4$.

Answer:

Set - builder notation: $\{y|y < 4\}$
Interval notation: $(-\infty,4)$
To graph the solution set, draw a number line. Put an open circle at 4 (because 4 is not included in the solution set) and shade the line to the left of 4.