Solve 26left(x-1right)=-65left(x+1right)-1/2left(x-78right)

$$26 \left( x-1 \right) = -65 \left( x+1 \right) - \frac{ 1 }{ 2 } \left( x-78 \right)$$

Solve for x

$$x=0$$

Steps for Solving Linear Equation

Use the distributive property to multiply 26 by x-1.

$$26x-26=-65\left(x+1\right)-\frac{1}{2}\left(x-78\right)$$

Use the distributive property to multiply -65 by x+1.

$$26x-26=-65x-65-\frac{1}{2}\left(x-78\right)$$

Use the distributive property to multiply -\frac{1}{2} by x-78.

$$26x-26=-65x-65-\frac{1}{2}x-\frac{1}{2}\left(-78\right)$$

Express -\frac{1}{2}\left(-78\right) as a single fraction.

$$26x-26=-65x-65-\frac{1}{2}x+\frac{-\left(-78\right)}{2}$$

Multiply -1 and -78 to get 78.

$$26x-26=-65x-65-\frac{1}{2}x+\frac{78}{2}$$

Divide 78 by 2 to get 39.

$$26x-26=-65x-65-\frac{1}{2}x+39$$

Combine -65x and -\frac{1}{2}x to get -\frac{131}{2}x.

$$26x-26=-\frac{131}{2}x-65+39$$

Add -65 and 39 to get -26.

$$26x-26=-\frac{131}{2}x-26$$

Add \frac{131}{2}x to both sides.

$$26x-26+\frac{131}{2}x=-26$$

Combine 26x and \frac{131}{2}x to get \frac{183}{2}x.

$$\frac{183}{2}x-26=-26$$

Add 26 to both sides.

$$\frac{183}{2}x=-26+26$$

Add -26 and 26 to get 0.

$$\frac{183}{2}x=0$$

Product of two numbers is equal to 0 if at least one of them is 0. Since \frac{183}{2} is not equal to 0, x must be equal to 0.

$$x=0$$