Whakaoti i te {l}{{(2x+1)}{(2x+6)}-7{(x-2)}=4{(x+1)}{(x-1)}-9x}{y=pi}{z=y}{a=z}{b=a}{text{Solvefor}ctext{where}}{c=b}

$$\left. \begin{array} { l } { {(2 x + 1)} {(2 x + 6)} - 7 {(x - 2)} = 4 {(x + 1)} {(x - 1)} - 9 x }\\ { y = \pi }\\ { z = y }\\ { a = z }\\ { b = a }\\ { \text{Solve for } c \text{ where} } \\ { c = b } \end{array} \right.$$

Whakaoti mō x, y, z, a, b, c

$$c=\pi \approx 3.141592654$$

Ngā Upane Otinga

Whakaarohia te whārite tuatahi. Whakamahia te āhuatanga tuaritanga hei whakarea te 2x+1 ki te 2x+6 ka whakakotahi i ngā kupu rite.

$$4x^{2}+14x+6-7\left(x-2\right)=4\left(x+1\right)\left(x-1\right)-9x$$

Whakamahia te āhuatanga tohatoha hei whakarea te -7 ki te x-2.

$$4x^{2}+14x+6-7x+14=4\left(x+1\right)\left(x-1\right)-9x$$

Pahekotia te 14x me -7x, ka 7x.

$$4x^{2}+7x+6+14=4\left(x+1\right)\left(x-1\right)-9x$$

Tāpirihia te 6 ki te 14, ka 20.

$$4x^{2}+7x+20=4\left(x+1\right)\left(x-1\right)-9x$$

Whakamahia te āhuatanga tohatoha hei whakarea te 4 ki te x+1.

$$4x^{2}+7x+20=\left(4x+4\right)\left(x-1\right)-9x$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 4x+4 ki te x-1 ka whakakotahi i ngā kupu rite.

$$4x^{2}+7x+20=4x^{2}-4-9x$$

Tangohia te 4x^{2} mai i ngā taha e rua.

$$4x^{2}+7x+20-4x^{2}=-4-9x$$

Pahekotia te 4x^{2} me -4x^{2}, ka 0.

$$7x+20=-4-9x$$

Me tāpiri te 9x ki ngā taha e rua.

$$7x+20+9x=-4$$

Pahekotia te 7x me 9x, ka 16x.

$$16x+20=-4$$

Tangohia te 20 mai i ngā taha e rua.

$$16x=-4-20$$

Tangohia te 20 i te -4, ka -24.

$$16x=-24$$

Whakawehea ngā taha e rua ki te 16.

$$x=\frac{-24}{16}$$

Whakahekea te hautanga \frac{-24}{16} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 8.

$$x=-\frac{3}{2}$$

Kua oti te pūnaha te whakatau.

$$x=-\frac{3}{2} y=\pi z=\pi a=\pi b=\pi c=\pi$$