Solve 2.6left(x-1right)=-6.5left(x+1right)-1/2left(x-7.8right)

$$2.6 \left( x-1 \right) = -6.5 \left( x+1 \right) - \frac{ 1 }{ 2 } \left( x-7.8 \right)$$

Solve for x

$$x=0$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2.6 by x-1.

$$2.6x-2.6=-6.5\left(x+1\right)-\frac{1}{2}\left(x-7.8\right)$$

Use the distributive property to multiply -6.5 by x+1.

$$2.6x-2.6=-6.5x-6.5-\frac{1}{2}\left(x-7.8\right)$$

Use the distributive property to multiply -\frac{1}{2} by x-7.8.

$$2.6x-2.6=-6.5x-6.5-\frac{1}{2}x-\frac{1}{2}\left(-7.8\right)$$

Convert decimal number -7.8 to fraction -\frac{78}{10}. Reduce the fraction -\frac{78}{10} to lowest terms by extracting and canceling out 2.

$$2.6x-2.6=-6.5x-6.5-\frac{1}{2}x-\frac{1}{2}\left(-\frac{39}{5}\right)$$

Multiply -\frac{1}{2} times -\frac{39}{5} by multiplying numerator times numerator and denominator times denominator.

$$2.6x-2.6=-6.5x-6.5-\frac{1}{2}x+\frac{-\left(-39\right)}{2\times 5}$$

Do the multiplications in the fraction \frac{-\left(-39\right)}{2\times 5}.

$$2.6x-2.6=-6.5x-6.5-\frac{1}{2}x+\frac{39}{10}$$

Combine -6.5x and -\frac{1}{2}x to get -7x.

$$2.6x-2.6=-7x-6.5+\frac{39}{10}$$

Convert decimal number -6.5 to fraction -\frac{65}{10}. Reduce the fraction -\frac{65}{10} to lowest terms by extracting and canceling out 5.

$$2.6x-2.6=-7x-\frac{13}{2}+\frac{39}{10}$$

Least common multiple of 2 and 10 is 10. Convert -\frac{13}{2} and \frac{39}{10} to fractions with denominator 10.

$$2.6x-2.6=-7x-\frac{65}{10}+\frac{39}{10}$$

Since -\frac{65}{10} and \frac{39}{10} have the same denominator, add them by adding their numerators.

$$2.6x-2.6=-7x+\frac{-65+39}{10}$$

Add -65 and 39 to get -26.

$$2.6x-2.6=-7x+\frac{-26}{10}$$

Reduce the fraction \frac{-26}{10} to lowest terms by extracting and canceling out 2.

$$2.6x-2.6=-7x-\frac{13}{5}$$

Add 7x to both sides.

$$2.6x-2.6+7x=-\frac{13}{5}$$

Combine 2.6x and 7x to get 9.6x.

$$9.6x-2.6=-\frac{13}{5}$$

Add 2.6 to both sides.

$$9.6x=-\frac{13}{5}+2.6$$

Add -\frac{13}{5} and 2.6 to get 0.

$$9.6x=0$$

Product of two numbers is equal to 0 if at least one of them is 0. Since 9.6 is not equal to 0, x must be equal to 0.

$$x=0$$