Solve 7.7+2/7-frac{2{1+x}}=1

$$7.7 + \frac { 2 } { 7 - \frac { 2 } { 1 + x } } = 1$$

Solve for x

$$x=-\frac{355}{489}\approx -0.72597137$$

Steps for Solving Linear Equation

To add or subtract expressions, expand them to make their denominators the same. Multiply 7 times \frac{1+x}{1+x}.

$$7.7+\frac{2}{\frac{7\left(1+x\right)}{1+x}-\frac{2}{1+x}}=1$$

Since \frac{7\left(1+x\right)}{1+x} and \frac{2}{1+x} have the same denominator, subtract them by subtracting their numerators.

$$7.7+\frac{2}{\frac{7\left(1+x\right)-2}{1+x}}=1$$

Do the multiplications in 7\left(1+x\right)-2.

$$7.7+\frac{2}{\frac{7+7x-2}{1+x}}=1$$

Combine like terms in 7+7x-2.

$$7.7+\frac{2}{\frac{5+7x}{1+x}}=1$$

Variable x cannot be equal to -1 since division by zero is not defined. Divide 2 by \frac{5+7x}{1+x} by multiplying 2 by the reciprocal of \frac{5+7x}{1+x}.

$$7.7+\frac{2\left(1+x\right)}{5+7x}=1$$

Use the distributive property to multiply 2 by 1+x.

$$7.7+\frac{2+2x}{5+7x}=1$$

Subtract 7.7 from both sides.

$$\frac{2+2x}{5+7x}=1-7.7$$

Subtract 7.7 from 1 to get -6.7.

$$\frac{2+2x}{5+7x}=-6.7$$

Variable x cannot be equal to -\frac{5}{7} since division by zero is not defined. Multiply both sides of the equation by 7x+5.

$$2+2x=-6.7\left(7x+5\right)$$

Use the distributive property to multiply -6.7 by 7x+5.

$$2+2x=-46.9x-33.5$$

Add 46.9x to both sides.

$$2+2x+46.9x=-33.5$$

Combine 2x and 46.9x to get 48.9x.

$$2+48.9x=-33.5$$

Subtract 2 from both sides.

$$48.9x=-33.5-2$$

Subtract 2 from -33.5 to get -35.5.

$$48.9x=-35.5$$

Divide both sides by 48.9.

$$x=\frac{-35.5}{48.9}$$

Expand \frac{-35.5}{48.9} by multiplying both numerator and the denominator by 10.

$$x=\frac{-355}{489}$$

Fraction \frac{-355}{489} can be rewritten as -\frac{355}{489} by extracting the negative sign.

$$x=-\frac{355}{489}$$