Solve -7/9x+1=-8/10x-1/2

$$- \frac { 7 } { 9 } x + 1 = - \frac { 8 } { 10 } x - \frac { 1 } { 2 }$$

Solve for x

$$x = -\frac{135}{2} = -67\frac{1}{2} = -67.5$$

Steps for Solving Linear Equation

Reduce the fraction \frac{8}{10} to lowest terms by extracting and canceling out 2.

$$-\frac{7}{9}x+1=-\frac{4}{5}x-\frac{1}{2}$$

Add \frac{4}{5}x to both sides.

$$-\frac{7}{9}x+1+\frac{4}{5}x=-\frac{1}{2}$$

Combine -\frac{7}{9}x and \frac{4}{5}x to get \frac{1}{45}x.

$$\frac{1}{45}x+1=-\frac{1}{2}$$

Subtract 1 from both sides.

$$\frac{1}{45}x=-\frac{1}{2}-1$$

Convert 1 to fraction \frac{2}{2}.

$$\frac{1}{45}x=-\frac{1}{2}-\frac{2}{2}$$

Since -\frac{1}{2} and \frac{2}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{45}x=\frac{-1-2}{2}$$

Subtract 2 from -1 to get -3.

$$\frac{1}{45}x=-\frac{3}{2}$$

Multiply both sides by 45, the reciprocal of \frac{1}{45}.

$$x=-\frac{3}{2}\times 45$$

Express -\frac{3}{2}\times 45 as a single fraction.

$$x=\frac{-3\times 45}{2}$$

Multiply -3 and 45 to get -135.

$$x=\frac{-135}{2}$$

Fraction \frac{-135}{2} can be rewritten as -\frac{135}{2} by extracting the negative sign.

$$x=-\frac{135}{2}$$