Whakaoti i te 3/7(x+3)+5=3x+2?

$$\frac { 3 } { 7 } ( x + 3 ) + 5 = 3 x + 2 ?$$

Whakaoti mō x

$$x = \frac{5}{3} = 1\frac{2}{3} \approx 1.666666667$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{3}{7} ki te x+3.

$$\frac{3}{7}x+\frac{3}{7}\times 3+5=3x+2$$

Tuhia te \frac{3}{7}\times 3 hei hautanga kotahi.

$$\frac{3}{7}x+\frac{3\times 3}{7}+5=3x+2$$

Whakareatia te 3 ki te 3, ka 9.

$$\frac{3}{7}x+\frac{9}{7}+5=3x+2$$

Me tahuri te 5 ki te hautau \frac{35}{7}.

$$\frac{3}{7}x+\frac{9}{7}+\frac{35}{7}=3x+2$$

Tā te mea he rite te tauraro o \frac{9}{7} me \frac{35}{7}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{3}{7}x+\frac{9+35}{7}=3x+2$$

Tāpirihia te 9 ki te 35, ka 44.

$$\frac{3}{7}x+\frac{44}{7}=3x+2$$

Tangohia te 3x mai i ngā taha e rua.

$$\frac{3}{7}x+\frac{44}{7}-3x=2$$

Pahekotia te \frac{3}{7}x me -3x, ka -\frac{18}{7}x.

$$-\frac{18}{7}x+\frac{44}{7}=2$$

Tangohia te \frac{44}{7} mai i ngā taha e rua.

$$-\frac{18}{7}x=2-\frac{44}{7}$$

Me tahuri te 2 ki te hautau \frac{14}{7}.

$$-\frac{18}{7}x=\frac{14}{7}-\frac{44}{7}$$

Tā te mea he rite te tauraro o \frac{14}{7} me \frac{44}{7}, me tango rāua mā te tango i ō raua taurunga.

$$-\frac{18}{7}x=\frac{14-44}{7}$$

Tangohia te 44 i te 14, ka -30.

$$-\frac{18}{7}x=-\frac{30}{7}$$

Me whakarea ngā taha e rua ki te -\frac{7}{18}, te tau utu o -\frac{18}{7}.

$$x=-\frac{30}{7}\left(-\frac{7}{18}\right)$$

Me whakarea te -\frac{30}{7} ki te -\frac{7}{18} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$x=\frac{-30\left(-7\right)}{7\times 18}$$

Mahia ngā whakarea i roto i te hautanga \frac{-30\left(-7\right)}{7\times 18}.

$$x=\frac{210}{126}$$

Whakahekea te hautanga \frac{210}{126} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 42.

$$x=\frac{5}{3}$$