Issolvi x/a+1/2a=2x-3/2a+2(1-a)

$$\frac { x } { a } + \frac { 1 } { 2 } a = 2 x - \frac { 3 } { 2 } a + 2 ( 1 - a )$$

Solvi għal x (complex solution)

$$\left\{\begin{matrix}x=2a\text{, }&a\neq 0\\x\in \mathrm{C}\text{, }&a=\frac{1}{2}\end{matrix}\right.$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Immultiplika ż-żewġ naħat tal-ekwazzjoni b'2a, l-inqas denominatur komuni ta' a,2.

$$2x+\frac{1}{2}a\times 2a=2x\times 2a-\frac{3}{2}a\times 2a+2\left(1-a\right)\times 2a$$

Immultiplika a u a biex tikseb a^{2}.

$$2x+\frac{1}{2}a^{2}\times 2=2x\times 2a-\frac{3}{2}a\times 2a+2\left(1-a\right)\times 2a$$

Immultiplika \frac{1}{2} u 2 biex tikseb 1.

$$2x+a^{2}=2x\times 2a-\frac{3}{2}a\times 2a+2\left(1-a\right)\times 2a$$

Immultiplika a u a biex tikseb a^{2}.

$$2x+a^{2}=2x\times 2a-\frac{3}{2}a^{2}\times 2+2\left(1-a\right)\times 2a$$

Immultiplika 2 u 2 biex tikseb 4.

$$2x+a^{2}=4xa-\frac{3}{2}a^{2}\times 2+2\left(1-a\right)\times 2a$$

Immultiplika -\frac{3}{2} u 2 biex tikseb -3.

$$2x+a^{2}=4xa-3a^{2}+2\left(1-a\right)\times 2a$$

Immultiplika 2 u 2 biex tikseb 4.

$$2x+a^{2}=4xa-3a^{2}+4\left(1-a\right)a$$

Uża l-propjetà distributtiva biex timmultiplika 4 b'1-a.

$$2x+a^{2}=4xa-3a^{2}+\left(4-4a\right)a$$

Uża l-propjetà distributtiva biex timmultiplika 4-4a b'a.

$$2x+a^{2}=4xa-3a^{2}+4a-4a^{2}$$

Ikkombina -3a^{2} u -4a^{2} biex tikseb -7a^{2}.

$$2x+a^{2}=4xa-7a^{2}+4a$$

Naqqas 4xa miż-żewġ naħat.

$$2x+a^{2}-4xa=-7a^{2}+4a$$

Naqqas a^{2} miż-żewġ naħat.

$$2x-4xa=-7a^{2}+4a-a^{2}$$

Ikkombina -7a^{2} u -a^{2} biex tikseb -8a^{2}.

$$2x-4xa=-8a^{2}+4a$$

Ikkombina t-termini kollha li fihom x.

$$\left(2-4a\right)x=-8a^{2}+4a$$

L-ekwazzjoni hija f'forma standard.

$$\left(2-4a\right)x=4a-8a^{2}$$

Iddividi ż-żewġ naħat b'2-4a.

$$\frac{\left(2-4a\right)x}{2-4a}=\frac{4a\left(1-2a\right)}{2-4a}$$

Meta tiddividi b'2-4a titneħħa l-multiplikazzjoni b'2-4a.

$$x=\frac{4a\left(1-2a\right)}{2-4a}$$

Iddividi 4a\left(1-2a\right) b'2-4a.

$$x=2a$$

Solvi għal x

$$\left\{\begin{matrix}x=2a\text{, }&a\neq 0\\x\in \mathrm{R}\text{, }&a=\frac{1}{2}\end{matrix}\right.$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Immultiplika ż-żewġ naħat tal-ekwazzjoni b'2a, l-inqas denominatur komuni ta' a,2.

$$2x+\frac{1}{2}a\times 2a=2x\times 2a-\frac{3}{2}a\times 2a+2\left(1-a\right)\times 2a$$

Immultiplika a u a biex tikseb a^{2}.

$$2x+\frac{1}{2}a^{2}\times 2=2x\times 2a-\frac{3}{2}a\times 2a+2\left(1-a\right)\times 2a$$

Immultiplika \frac{1}{2} u 2 biex tikseb 1.

$$2x+a^{2}=2x\times 2a-\frac{3}{2}a\times 2a+2\left(1-a\right)\times 2a$$

Immultiplika a u a biex tikseb a^{2}.

$$2x+a^{2}=2x\times 2a-\frac{3}{2}a^{2}\times 2+2\left(1-a\right)\times 2a$$

Immultiplika 2 u 2 biex tikseb 4.

$$2x+a^{2}=4xa-\frac{3}{2}a^{2}\times 2+2\left(1-a\right)\times 2a$$

Immultiplika -\frac{3}{2} u 2 biex tikseb -3.

$$2x+a^{2}=4xa-3a^{2}+2\left(1-a\right)\times 2a$$

Immultiplika 2 u 2 biex tikseb 4.

$$2x+a^{2}=4xa-3a^{2}+4\left(1-a\right)a$$

Uża l-propjetà distributtiva biex timmultiplika 4 b'1-a.

$$2x+a^{2}=4xa-3a^{2}+\left(4-4a\right)a$$

Uża l-propjetà distributtiva biex timmultiplika 4-4a b'a.

$$2x+a^{2}=4xa-3a^{2}+4a-4a^{2}$$

Ikkombina -3a^{2} u -4a^{2} biex tikseb -7a^{2}.

$$2x+a^{2}=4xa-7a^{2}+4a$$

Naqqas 4xa miż-żewġ naħat.

$$2x+a^{2}-4xa=-7a^{2}+4a$$

Naqqas a^{2} miż-żewġ naħat.

$$2x-4xa=-7a^{2}+4a-a^{2}$$

Ikkombina -7a^{2} u -a^{2} biex tikseb -8a^{2}.

$$2x-4xa=-8a^{2}+4a$$

Ikkombina t-termini kollha li fihom x.

$$\left(2-4a\right)x=-8a^{2}+4a$$

L-ekwazzjoni hija f'forma standard.

$$\left(2-4a\right)x=4a-8a^{2}$$

Iddividi ż-żewġ naħat b'2-4a.

$$\frac{\left(2-4a\right)x}{2-4a}=\frac{4a\left(1-2a\right)}{2-4a}$$

Meta tiddividi b'2-4a titneħħa l-multiplikazzjoni b'2-4a.

$$x=\frac{4a\left(1-2a\right)}{2-4a}$$

Iddividi 4a\left(1-2a\right) b'2-4a.

$$x=2a$$

Solvi għal a

$$\left\{\begin{matrix}\\a=\frac{1}{2}=0.5\text{, }&\text{unconditionally}\\a=\frac{x}{2}\text{, }&x\neq 0\end{matrix}\right.$$