Given QR is congrent to LN and QR = 4x + 2 and LN = x + 7.
So, QR = LN
Hence, we can set up an equation as following:
4x + 2 = x + 7
4x + 2 - x = x + 7 - x Subtract x from each sides.
3x + 2 = 7 By simplifying.
3x + 2 - 2 = 7 - 2 Subtract 2 from each sides.
3x = 5
[tex] \frac{3x}{3} =\frac{5}{3} [/tex] Divide each sides by 3 to isolate x.
So, [tex] x=\frac{5}{3} [/tex]
Next step is to plug in [tex] x=\frac{5}{3} [/tex] in QR = 4x+2 to get length of QR.
So, [tex] QR = 4(\frac{5}{3})+2 [/tex]
[tex] =(\frac{20}{3})+\frac{2}{1} [/tex] Since 2 can be written as 2/1.
By multiplying the second fraction by the common denominator 3.
[tex] =(\frac{20}{3})+\frac{2*3}{1*3} [/tex]
[tex] =(\frac{20}{3})+\frac{6}{3} [/tex] By simplifying the second fraction.
[tex] =(\frac{26}{3}) [/tex]
So, [tex] QR=\frac{26}{3} [/tex]
