Solve (x+1)div(x-6)=7

$$(x+1) \div (x-6)=7$$

Solve for x

$$x = \frac{43}{6} = 7\frac{1}{6} \approx 7.166666667$$

Steps for Solving Linear Equation

Variable x cannot be equal to 6 since division by zero is not defined. Multiply both sides of the equation by x-6.

$$x+1=7\left(x-6\right)$$

Use the distributive property to multiply 7 by x-6.

$$x+1=7x-42$$

Subtract 7x from both sides.

$$x+1-7x=-42$$

Combine x and -7x to get -6x.

$$-6x+1=-42$$

Subtract 1 from both sides.

$$-6x=-42-1$$

Subtract 1 from -42 to get -43.

$$-6x=-43$$

Divide both sides by -6.

$$x=\frac{-43}{-6}$$

Fraction \frac{-43}{-6} can be simplified to \frac{43}{6} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{43}{6}$$