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Chapter 6: Problem 55

Solve and check each equation. \(\frac{3 x}{5}-x=\frac{x}{10}-\frac{5}{2}\)

Short Answer

Expert verified
-25/16

Step by step solution

01

Simplify the equations

To simplify, we first get rid of the fractions by multiplying all terms by the lowest common multiple of 5 and 10, which is 10. This gives us: \(6x - 10x = x - 25\)
02

Solve for x

Now we just need to combine like terms and solve for x by adding 10x to both sides also. This will give us: \(6x - 10x +10x = x + 10x -25\), \nwhich simplifies to: \(16x = -25\).\nSolving for x we divide both sides of the equation by 16 giving us: \(x = -\frac{25}{16}\)
03

Verify your answer

We verify the solution by substituting \(x = -\frac{25}{16}\) back into the original equation and ensuring that both sides of the equation is equal.

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