Whakaoti i te 2(3/2x-21/10)+17/10geq2(12/5x-frac{7}{2})

$$2 ( \frac { 3 } { 2 } x - \frac { 21 } { 10 } ) + \frac { 17 } { 10 } \geq 2 ( \frac { 12 } { 5 } x - \frac { 7 } { 2 } )$$

Whakaoti mō x

$$x\leq \frac{5}{2}$$

Ngā Upane Otinga

Whakamahia te āhuatanga tohatoha hei whakarea te 2 ki te \frac{3}{2}x-\frac{21}{10}.

$$2\times \frac{3}{2}x+2\left(-\frac{21}{10}\right)+\frac{17}{10}\geq 2\left(\frac{12}{5}x-\frac{7}{2}\right)$$

Me whakakore te 2 me te 2.

$$3x+2\left(-\frac{21}{10}\right)+\frac{17}{10}\geq 2\left(\frac{12}{5}x-\frac{7}{2}\right)$$

Tuhia te 2\left(-\frac{21}{10}\right) hei hautanga kotahi.

$$3x+\frac{2\left(-21\right)}{10}+\frac{17}{10}\geq 2\left(\frac{12}{5}x-\frac{7}{2}\right)$$

Whakareatia te 2 ki te -21, ka -42.

$$3x+\frac{-42}{10}+\frac{17}{10}\geq 2\left(\frac{12}{5}x-\frac{7}{2}\right)$$

Whakahekea te hautanga \frac{-42}{10} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$3x-\frac{21}{5}+\frac{17}{10}\geq 2\left(\frac{12}{5}x-\frac{7}{2}\right)$$

Ko te maha noa iti rawa atu o 5 me 10 ko 10. Me tahuri -\frac{21}{5} me \frac{17}{10} ki te hautau me te tautūnga 10.

$$3x-\frac{42}{10}+\frac{17}{10}\geq 2\left(\frac{12}{5}x-\frac{7}{2}\right)$$

Tā te mea he rite te tauraro o -\frac{42}{10} me \frac{17}{10}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$3x+\frac{-42+17}{10}\geq 2\left(\frac{12}{5}x-\frac{7}{2}\right)$$

Tāpirihia te -42 ki te 17, ka -25.

$$3x+\frac{-25}{10}\geq 2\left(\frac{12}{5}x-\frac{7}{2}\right)$$

Whakahekea te hautanga \frac{-25}{10} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 5.

$$3x-\frac{5}{2}\geq 2\left(\frac{12}{5}x-\frac{7}{2}\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2 ki te \frac{12}{5}x-\frac{7}{2}.

$$3x-\frac{5}{2}\geq 2\times \frac{12}{5}x+2\left(-\frac{7}{2}\right)$$

Tuhia te 2\times \frac{12}{5} hei hautanga kotahi.

$$3x-\frac{5}{2}\geq \frac{2\times 12}{5}x+2\left(-\frac{7}{2}\right)$$

Whakareatia te 2 ki te 12, ka 24.

$$3x-\frac{5}{2}\geq \frac{24}{5}x+2\left(-\frac{7}{2}\right)$$

Me whakakore te 2 me te 2.

$$3x-\frac{5}{2}\geq \frac{24}{5}x-7$$

Tangohia te \frac{24}{5}x mai i ngā taha e rua.

$$3x-\frac{5}{2}-\frac{24}{5}x\geq -7$$

Pahekotia te 3x me -\frac{24}{5}x, ka -\frac{9}{5}x.

$$-\frac{9}{5}x-\frac{5}{2}\geq -7$$

Me tāpiri te \frac{5}{2} ki ngā taha e rua.

$$-\frac{9}{5}x\geq -7+\frac{5}{2}$$

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

$$-\frac{9}{5}x\geq -\frac{14}{2}+\frac{5}{2}$$

Tā te mea he rite te tauraro o -\frac{14}{2} me \frac{5}{2}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$-\frac{9}{5}x\geq \frac{-14+5}{2}$$

Tāpirihia te -14 ki te 5, ka -9.

$$-\frac{9}{5}x\geq -\frac{9}{2}$$

Me whakarea ngā taha e rua ki te -\frac{5}{9}, te tau utu o -\frac{9}{5}. I te mea he tōraro a -\frac{9}{5}, ka huri te ahunga koreōrite.

$$x\leq -\frac{9}{2}\left(-\frac{5}{9}\right)$$

Me whakarea te -\frac{9}{2} ki te -\frac{5}{9} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$x\leq \frac{-9\left(-5\right)}{2\times 9}$$

Mahia ngā whakarea i roto i te hautanga \frac{-9\left(-5\right)}{2\times 9}.

$$x\leq \frac{45}{18}$$

Whakahekea te hautanga \frac{45}{18} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 9.

$$x\leq \frac{5}{2}$$