Problem 51 Solve and check each equation. ... [FREE SOLUTION]

Chapter 6: Problem 51

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

Short Answer

Expert verified

The solution to the equation is \(y = -6\)

Step by step solution

Eliminate fractions

To make the equation easier to deal with, it's beneficial to eliminate the fractions. We can do this by finding the least common multiple (LCM) or least common denominator (LCD) of all the denominators present in the fractions. Here the LCD is 15, since both 3 and 5 divide into 15. If we multiply each term by 15, the fractions will be eliminated. So, \(15*\frac{y}{3} + 15*\frac{2}{5} = 15*\frac{y}{5} - 15*\frac{2}{5}\) equals to \(5y + 6 = 3y - 6\)

Combine like terms

Next step, isolate variable y by moving all the terms with y to one side. We'll subtract 3y from both sides to get \(5y - 3y + 6 = -6\), this simplifies to \(2y + 6 = -6\)

Isolate the variable

Finally, isolate the variable. To do this, subtract 6 from both sides. This gives us \(2y = -12\).

Solve for y

Divide both sides by 2 and we get \(y = -6\).

Check the solution

In the final step, we check the solution by substituting -6 for y in the original equation. \(\frac{-6}{3} + \frac{2}{5} = \frac{-6}{5} - \frac{2}{5}\) simplifies to \(-2 + 0.4 = -1.2 - 0.4\), which is true as both sides equal to -1.6

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91影视

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

Short Answer

Step by step solution

Eliminate fractions

Combine like terms

Isolate the variable

Solve for y

Check the solution

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