Solve for b

b=8+\frac{12}{x},x\neq 0

$b=8+x12 ,x=0$

Solve for x

x=-\frac{12}{8-b},b\neq 8

$x=−8−b12 ,b=8$

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bx-7=8x+5

Swap sides so that all variable terms are on the left hand side.

bx=8x+5+7

Add 7 to both sides.

bx=8x+12

Add 5 and 7 to get 12.

xb=8x+12

The equation is in standard form.

\frac{xb}{x}=\frac{8x+12}{x}

Divide both sides by x.

b=\frac{8x+12}{x}

Dividing by x undoes the multiplication by x.

b=8+\frac{12}{x}

Divide 8x+12 by x.

8x+5-bx=-7

Subtract bx from both sides.

8x-bx=-7-5

Subtract 5 from both sides.

8x-bx=-12

Subtract 5 from -7 to get -12.

\left(8-b\right)x=-12

Combine all terms containing x.

\frac{\left(8-b\right)x}{8-b}=\frac{-12}{8-b}

Divide both sides by 8-b.

x=\frac{-12}{8-b}

Dividing by 8-b undoes the multiplication by 8-b.

x=-\frac{12}{8-b}

Divide -12 by 8-b.

Examples

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{ x } ^ { 2 } - 4 x - 5 = 0

$x_{2}−4x−5=0$

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4 \sin \theta \cos \theta = 2 \sin \theta

$4sinθcosθ=2sinθ$

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$y=3x+4$

Arithmetic

699 * 533

$699∗533$

Matrix

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$[25 34 ][2−1 01 35 ]$

Simultaneous equation

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${8x+2y=467x+3y=47 $

Differentiation

\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }

$dxd (x−5)(3x_{2}−2) $

Integration

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$∫_{0}xe_{−x_{2}}dx$

Limits

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$x→−3lim x_{2}+2x−3x_{2}−9 $