Whakaoti i te 1/9[3x-6-5(7x/2-5)]+13(x-5)+1/4=0

$$\frac { 1 } { 9 } [ 3 x - 6 - 5 ( \frac { 7 x } { 2 } - 5 ) ] + 13 ( x - 5 ) + \frac { 1 } { 4 } = 0$$

Whakaoti mō x

$$x = \frac{11}{2} = 5\frac{1}{2} = 5.5$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te 36, arā, te tauraro pātahi he tino iti rawa te kitea o 9,2,4.

$$4\left(3x-6-5\left(\frac{7x}{2}-5\right)\right)+468\left(x-5\right)+9=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te 468 ki te x-5.

$$4\left(3x-6-5\left(\frac{7x}{2}-5\right)\right)+468x-2340+9=0$$

Tāpirihia te -2340 ki te 9, ka -2331.

$$4\left(3x-6-5\left(\frac{7x}{2}-5\right)\right)+468x-2331=0$$

Me tāpiri te 2331 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$4\left(3x-6-5\left(\frac{7x}{2}-5\right)\right)+468x=2331$$

Whakareatia ngā taha e rua o te whārite ki te 2.

$$8\left(3x-6-5\left(\frac{7x}{2}-5\right)\right)+936x=4662$$

Whakareatia ngā taha e rua o te whārite ki te 2.

$$16\left(3x-6-5\left(\frac{7x}{2}-5\right)\right)+1872x=9324$$

Whakamahia te āhuatanga tohatoha hei whakarea te -5 ki te \frac{7x}{2}-5.

$$16\left(3x-6-5\times \frac{7x}{2}+25\right)+1872x=9324$$

Tuhia te -5\times \frac{7x}{2} hei hautanga kotahi.

$$16\left(3x-6+\frac{-5\times 7x}{2}+25\right)+1872x=9324$$

Whakareatia te -5 ki te 7, ka -35.

$$16\left(3x-6+\frac{-35x}{2}+25\right)+1872x=9324$$

Tāpirihia te -6 ki te 25, ka 19.

$$16\left(3x+19+\frac{-35x}{2}\right)+1872x=9324$$

Whakamahia te āhuatanga tohatoha hei whakarea te 16 ki te 3x+19+\frac{-35x}{2}.

$$48x+304+16\times \frac{-35x}{2}+1872x=9324$$

Whakakorea atu te tauwehe pūnoa nui rawa 2 i roto i te 16 me te 2.

$$48x+304+8\left(-35\right)x+1872x=9324$$

Whakareatia te 8 ki te -35, ka -280.

$$48x+304-280x+1872x=9324$$

Pahekotia te 48x me -280x, ka -232x.

$$-232x+304+1872x=9324$$

Pahekotia te -232x me 1872x, ka 1640x.

$$1640x+304=9324$$

Tangohia te 304 mai i ngā taha e rua.

$$1640x=9324-304$$

Tangohia te 304 i te 9324, ka 9020.

$$1640x=9020$$

Whakawehea ngā taha e rua ki te 1640.

$$x=\frac{9020}{1640}$$

Whakahekea te hautanga \frac{9020}{1640} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 820.

$$x=\frac{11}{2}$$