Question

Point Q is on line segment \overline{PR}

PR

. Given QR=2x+4,

QR=2x+4, PQ=x,

PQ=x, and PR=4x-10,

PR=4x−10, determine the numerical length of \overline{PR}.

PR

.

Answer 1

Note that $PR=PQ+QR$

Substitute $PR=4x-10$ , $PQ=x$ , and $QR=2x+4$ into the relation:

$4x-10=x+2x+4$

Add like terms:

$4x-10=3x+4$

Subtract $3x$ from both sides:

$4x-10-3x=3x+4-3x$

Combine like terms:

$x-10=4$

Add $10$ to both sides:

$x=4+10$

Add the numbers:

$x=14$

Note that $PR=4x-10$

Substitute $x=14$ into the equation:

$PR=4(14)-10=46$

The numerical length of $\overline{PR}$ is $46$