Answer:
B.6
Step-by-step explanation:
3 + 2x + 22 = x + 17
Combine like terms
25 + 2x = x + 17
Subtract 17 from both sides
8 + 2x = x
Subtract 2x from both sides
8 = -x
Divide both sides by -1
x = -8
Substitute -8 for x in 2x + 22 to find value of QR
2(-8) + 22
Multiply
-16 + 22
Add
QR = 6
[tex]\sf \bf {\boxed {\mathbb {Given:}}}[/tex]
PQ = 3
QR = 2[tex]x[/tex] + 22
PR = [tex]x[/tex] + 17
[tex]\sf \bf {\boxed {\mathbb {To\:find:}}}[/tex]
The value of QR.
[tex]\sf \bf {\boxed {\mathbb {Solution:}}}[/tex]
[tex]\sf\purple{B. \:6}[/tex]
[tex]\sf \bf {\boxed {\mathbb {Step-by-step\:explanation:}}}[/tex]
From the figure, we have
PR = PQ + QR
➺[tex]\:x + 17 = 3 + 2x + 22[/tex]
➺[tex] \: x - 2x = 25 - 17[/tex]
➺[tex] \: - x = 8[/tex]
➺[tex] \: x = - 8[/tex]
Now,
QR = [tex]2x + 22[/tex]
Plugging in the value of [tex]x[/tex], we have
[tex] = \: 2 \times (- 8 )+ 22[/tex]
[tex] = \: - 16 + 22[/tex]
[tex] = \: 6[/tex]
[tex]\sf\pink{Therefore,\: the\: value\: of\: QR\: is\: 6.}[/tex]
[tex]\sf \bf {\boxed {\mathbb {To\:verify:}}}[/tex]
PR = PQ + QR
➺[tex]\:x + 17 = 3 + 6[/tex]
➺[tex] \: - 8 + 17 = 9[/tex]
➺[tex] \: 9 = 9[/tex]
➺ L. H. S. = R. H. S.
Hence verified.
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]
