Question

question
point o is on line segment $overline{np}$. given $np = 4x + 10, no = 4x$, and $op = x + 5$, determine the numerical length of $overline{np}$.
answer
attempt 1 out of 2
$np =$

Explanation:

Step1: Use segment - addition postulate

Since point O is on line segment $\overline{NP}$, we know that $NO + OP=NP$. Substitute the given expressions: $4x+(x + 5)=4x + 10$.

Step2: Simplify the left - hand side of the equation

Combine like terms: $4x+x+5=5x + 5$. So, $5x+5=4x + 10$.

Step3: Solve for x

Subtract $4x$ from both sides: $5x-4x+5=4x-4x + 10$, which gives $x+5=10$. Then subtract 5 from both sides: $x=10 - 5=5$.

Step4: Find the length of NP

Substitute $x = 5$ into the expression for $NP$. Since $NP=4x + 10$, then $NP=4\times5+10$. Calculate $4\times5+10=20 + 10=30$.

Answer:

$30$