Solve for x
x=6
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5\times 3+5\left(2x-7\right)\times \frac{2}{5}=5\left(2x-7\right)
Variable x cannot be equal to \frac{7}{2} since division by zero is not defined. Multiply both sides of the equation by 5\left(2x-7\right), the least common multiple of 2x-7,5.
15+5\left(2x-7\right)\times \frac{2}{5}=5\left(2x-7\right)
Multiply 5 and 3 to get 15.
15+2\left(2x-7\right)=5\left(2x-7\right)
Multiply 5 and \frac{2}{5} to get 2.
15+4x-14=5\left(2x-7\right)
Use the distributive property to multiply 2 by 2x-7.
1+4x=5\left(2x-7\right)
Subtract 14 from 15 to get 1.
1+4x=10x-35
Use the distributive property to multiply 5 by 2x-7.
1+4x-10x=-35
Subtract 10x from both sides.
1-6x=-35
Combine 4x and -10x to get -6x.
-6x=-35-1
Subtract 1 from both sides.
-6x=-36
Subtract 1 from -35 to get -36.
x=\frac{-36}{-6}
Divide both sides by -6.
x=6
Divide -36 by -6 to get 6.
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