Simplify the following expressions by reducing it to a single fraction: 2x-5/4 - 1-x/3 - x-4/2

Zidisha pande zote mbili kwa $2x$ kuondoa vigawe.

$$x(2x - 11) = 2 \times 3$$ $$2x^2 - 11x = 6$$

Panga upya mlinganyo kuwa fomu ya quadratic $ax^2 + bx + c = 0$.

$$2x^2 - 11x - 6 = 0$$

Tafuta namba mbili zinazozidisha hadi $2 \times (-6) = -12$ na kujumlisha hadi $-11$. Namba hizo ni $-12$ na 1.

$$2x^2 - 12x + x - 6 = 0$$

Toa $2x$ kama kigezo cha kawaida kutoka kwa maneno mawili ya kwanza na 1 kutoka kwa maneno mawili ya mwisho.

$$2x(x - 6) + 1(x - 6) = 0$$

Toa $(x - 6)$ kama kigezo cha kawaida.

$$(2x + 1)(x - 6) = 0$$

Hii inatoa suluhisho mbili zinazowezekana:

$$2x + 1 = 0 \implies 2x = -1 \implies x = -\frac{1}{2}$$ $$x - 6 = 0 \implies x = 6$$

Hoja ya logariti lazima iwe chanya.
Kwa $x = -\frac{1}{2}$:
$2x - 11 = 2\left(-\frac{1}{2}\right) - 11 = -1 - 11 = -12$. Hii ni hasi, hivyo $\log(-12)$ haijafafanuliwa.
$x = -\frac{1}{2}$. Hii ni hasi, hivyo $\log\left(-\frac{1}{2}\right)$ haijafafanuliwa.
Kwa hiyo, $x = -\frac{1}{2}$ si suluhisho halali.

Kwa $x = 6$:
$2x - 11 = 2(6) - 11 = 12 - 11 = 1$. Hii ni chanya.
$x = 6$. Hii ni chanya.
Hoja zote za logariti ni chanya, hivyo $x = 6$ ni suluhisho halali.

Thamani ya $x$ inayokidhi mlinganyo ni: