Question

(x+3)/7 -(2x-5)/3 = (3x-5)/5 -25

Answer 1

$\huge \boxed{\mathfrak{Question} \downarrow}$

$\large \sf\frac{ x+3 }{ 7 } - \frac{ (2x-5) }{ 3 } = \frac{ (3x-5) }{ 5 } -25$

$\huge \boxed{\mathfrak{Answer} \downarrow}$

$\large \boxed{ \bf \: x=25}$

$\huge \boxed{\mathfrak{Steps} \downarrow}$

$\large \sf \: \frac{ x+3 }{ 7 } - \frac{ (2x-5) }{ 3 } = \frac{ (3x-5) }{ 5 } -25$

Multiply both sides of the equation by 105, the least common multiple of 7,3,5.

$\large \sf \: 15\left(x+3\right)-35\left(2x-5\right)=21\left(3x-5\right)-2625$

Use the distributive property to multiply 15 by x+3.

$\large \sf \: 15x+45-35\left(2x-5\right)=21\left(3x-5\right)-2625$

Use the distributive property to multiply -35 by 2x-5.

$\large \sf \: 15x+45-70x+175=21\left(3x-5\right)-2625$

Combine 15x and -70x to get -55x.

$\large \sf \: -55x+45+175=21\left(3x-5\right)-2625$

Add 45 and 175 to get 220.

$\large \sf \: -55x+220=21\left(3x-5\right)-2625$

Use the distributive property to multiply 21 by 3x-5.

$\large \sf \: -55x+220=63x-105-2625$

Subtract 2625 from -105 to get -2730.

$\large \sf \: -55x+220=63x-2730$

Subtract 63x from both sides.

$\large \sf \: -55x+220-63x=-2730$

Combine -55x and -63x to get -118x.

$\large \sf \: -118x+220=-2730$

Subtract 220 from both sides.

$\large \sf-118x=-2730-220$

Subtract 220 from -2730 to get -2950.

$\large \sf \: -118x=-2950$

Divide both sides by -118.

$\large \sf \: x=\frac{-2950}{-118}$

Divide -2950 by -118 to get 25.

$\large \boxed{ \bf \: x=25}$