Question

How do you graph and solve |3y+2|=|2y−5|?

Answer 1

Answer : y1 = - 7, y2 = 0.6

Step by step explanation :

$|3y + 2| = |2y - 5|$

Split the equation into two possible cases.

$= > 3y + 2 = 2y - 5 \: \: \: \: - eq1\\ \: \: \: \: \: \: \: \: 3y + 2 = - (2y - 5) \: \: \: - eq2$

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Solve the equation for y (Eq-1). Move variable to the left side and change its sign. Move constant to the right side and change its sign.

$= > 3y - 2y = - 5 - 2$

Collect the like terms and calculate the difference.

$= > y = - 7$

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Solve the equation for y (Eq - 2).When there is a "-" in front of the parenthesis change the sign of each term in parenthesis.

$= > 3y + 2 = - 2y + 5$

Move variable to the left side and change its sign. Move constant to the right side and change its sign.

$= > 3y + 2y = 5 - 2$

Collect the like terms and subtract the numbers.

$= > 5y = 3$

$= > y1 = - 7 \\ \: \: \: \: \: \: \: \: y2 = 0.6$

Divide both sides of the equation by 3.

$= > y = \frac{3}{5}$

The final solutions are

$= > y1 = - 7 \\ \: \: \: \: \: \: \: \: y2 = \frac{3}{5}$