Issolvi (x-1)(x^2+x+1)-9-2xleq(x-1)^3+x(3x-2)

$$( x - 1 ) ( x ^ { 2 } + x + 1 ) - 9 - 2 x \leq ( x - 1 ) ^ { 3 } + x ( 3 x - 2 )$$

Solvi għal x

$$x\geq -3$$

Passi tas-Soluzzjonijiet

Uża l-propjetà distributtiva biex timmultiplika x-1 b'x^{2}+x+1 u kkombina termini simili.

$$x^{3}-1-9-2x\leq \left(x-1\right)^{3}+x\left(3x-2\right)$$

Naqqas 9 minn -1 biex tikseb -10.

$$x^{3}-10-2x\leq \left(x-1\right)^{3}+x\left(3x-2\right)$$

Uża teorema binomjali \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} biex tespandi \left(x-1\right)^{3}.

$$x^{3}-10-2x\leq x^{3}-3x^{2}+3x-1+x\left(3x-2\right)$$

Uża l-propjetà distributtiva biex timmultiplika x b'3x-2.

$$x^{3}-10-2x\leq x^{3}-3x^{2}+3x-1+3x^{2}-2x$$

Ikkombina -3x^{2} u 3x^{2} biex tikseb 0.

$$x^{3}-10-2x\leq x^{3}+3x-1-2x$$

Ikkombina 3x u -2x biex tikseb x.

$$x^{3}-10-2x\leq x^{3}+x-1$$

Naqqas x^{3} miż-żewġ naħat.

$$x^{3}-10-2x-x^{3}\leq x-1$$

Ikkombina x^{3} u -x^{3} biex tikseb 0.

$$-10-2x\leq x-1$$

Naqqas x miż-żewġ naħat.

$$-10-2x-x\leq -1$$

Ikkombina -2x u -x biex tikseb -3x.

$$-10-3x\leq -1$$

Żid 10 maż-żewġ naħat.

$$-3x\leq -1+10$$

Żid -1 u 10 biex tikseb 9.

$$-3x\leq 9$$

Iddividi ż-żewġ naħat b'-3. Peress li -3 huwa negattiv, id-direzzjoni tal-inugwaljanza inbidlet.

$$x\geq \frac{9}{-3}$$

Iddividi 9 b'-3 biex tikseb-3.

$$x\geq -3$$