Question

use the number line below, where rs = 7y + 5, st = 3y + 7, and rt = 15y - 18. a. what is the value of y? b. find rs, st, and rt. y = □ (type an integer or a decimal.)

Explanation:

Step1: Apply segment - addition postulate

Since on a number line, $RT=RS + ST$, we substitute the given expressions: $15y-18=(7y + 5)+(3y + 7)$.

Step2: Simplify the right - hand side

Combine like terms on the right - hand side: $(7y+3y)+(5 + 7)=10y+12$. So the equation becomes $15y-18=10y + 12$.

Step3: Isolate the variable terms

Subtract $10y$ from both sides: $15y-10y-18=10y-10y + 12$, which simplifies to $5y-18=12$.

Step4: Isolate the variable

Add 18 to both sides: $5y-18 + 18=12+18$, getting $5y=30$.

Step5: Solve for y

Divide both sides by 5: $\frac{5y}{5}=\frac{30}{5}$, so $y = 6$.

Answer:

$y = 6$