Question

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

Answer 1

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

`\large \sf( x+3 )/( 7 ) - ( (2x-5) )/( 3 ) = ( (3x-5) )/( 5 ) -25 \\`

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

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

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

`\large \sf \: ( x+3 )/( 7 ) - ( (2x-5) )/( 3 ) = ( (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=(-2950)/(-118) \\`

Divide -2950 by -118 to get 25.

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