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QuestionSolve the equation: 2y−35+910=4y+510\frac{2y-3}{5} + \frac{9}{10} = \frac{4y+5}{10}.

Studdy Solution

STEP 1

Assumptions1. The equation is a linear equation in one variable, y. . The equation is in the form of fractions, and we need to solve for y.

STEP 2

The first step in solving this equation is to eliminate the fractions. We can do this by finding the least common multiple (LCM) of the denominators (5,10, and10), which is10. Multiply each term by10.
10×(2y−5)+10×(910)=10×(4y+510)10 \times \left(\frac{2 y-}{5}\right) +10 \times \left(\frac{9}{10}\right) =10 \times \left(\frac{4 y+5}{10}\right)

STEP 3

implify each term.
y−6+9=y+5 y -6 +9 = y +5

STEP 4

Now, we can simplify the equation by combining like terms on each side.
4y+3=4y+4 y +3 =4 y +

STEP 5

Next, we subtract 4y4 y from both sides of the equation to isolate y.
3=53 =5

STEP 6

This equation is not possible, as3 does not equal5. Therefore, there is no solution to the given equation.

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