What is the answer to (x+6)/(3-2x)=-1 ?

The answer to (x+6)/(3-2x)=-1 is x=9

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(x+6)/(3-2x)=-1

\frac{x + 6}{3 - 2 x} = - 1

x = 9

Solution steps

\frac{x + 6}{3 - 2 x} = - 1

Multiply both sides by

3 - 2 x

x + 6 = - (3 - 2 x)

Expand

- (3 - 2 x) : - 3 + 2 x

x + 6 = - 3 + 2 x

Move

6

to the right side

x = 2 x - 9

Move

2 x

to the left side

- x = - 9

Divide both sides by

- 1

x = 9

Verify Solutions

Find undefined (singularity) points:

x = \frac{3}{2}

Combine undefined points with solutions:

x = 9

\frac{3 x + 2}{x - 1} - \frac{6}{5} = 0

\frac{( 4 x + 1 )}{( 2 x + 2 )} = 128

\frac{1}{6 x} = \frac{4}{15}

\frac{A X + B}{X} = \frac{CX}{D}

\frac{750}{x - 750} = 2.083