Question

solve the inequality and graph the solution. 12 > 4(r + 15) - 64. plot the endpoints. select an endpoint to change it from closed to open. select the middle of the segment, ray, or line to delete it.

Explanation:

Step1: Expand the right - hand side

Expand $4(r + 15)-64$ using the distributive property $a(b + c)=ab+ac$. So $4(r + 15)-64=4r+60 - 64=4r - 4$. The inequality becomes $12>4r - 4$.

Step2: Add 4 to both sides

To isolate the term with $r$, add 4 to both sides of the inequality. $12 + 4>4r-4 + 4$, which simplifies to $16>4r$.

Step3: Divide both sides by 4

Divide both sides of the inequality $16>4r$ by 4. $\frac{16}{4}>\frac{4r}{4}$, so $4>r$ or $r < 4$.

Step4: Graph the solution

On the number - line, plot an open circle at 4 (since the inequality is $r < 4$, not $r\leq4$) and draw a ray to the left of 4 to represent all the values of $r$ that satisfy the inequality.

Answer:

The solution of the inequality is $r < 4$. On the number - line, there is an open circle at 4 and a ray extending to the left.