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QuestionSolve the equation y−4y+3=−5(y+3.4)y - 4y + 3 = -5(y + 3.4) and simplify to an integer, fraction, or decimal (2 decimal places).

Studdy Solution

STEP 1

Assumptions1. The equation is a linear equation in one variable, y. . The equation is given by y−4y+3=−5(y+3.4)y-4y+3=-5(y+3.4)3. The solution should be expressed as an integer, a simplified fraction, or a decimal rounded to two decimal places.

STEP 2

First, simplify the left side of the equation by combining like terms.
y−4y+=−y+y-4y+ = -y+

STEP 3

Next, distribute the -5 on the right side of the equation.
−5(y+3.)=−5y−17-5(y+3.) = -5y-17

STEP 4

Now, set the simplified left side of the equation equal to the simplified right side of the equation.
−y+3=−y−17-y+3=-y-17

STEP 5

To isolate y, add5y to both sides of the equation.
−y+5y+3=−5y+5y−17-y+5y+3=-5y+5y-17

STEP 6

implify both sides of the equation.
4y+3=−174y+3=-17

STEP 7

Next, subtract3 from both sides of the equation to isolate the term with y on one side.
4y+3−3=−17−34y+3-3=-17-3

STEP 8

implify both sides of the equation.
4y=−204y=-20

STEP 9

Finally, divide both sides of the equation by4 to solve for y.
y=−204y=\frac{-20}{4}

STEP 10

implify the right side of the equation to find the solution for y.
y=−5y=-5The solution to the equation is y=-5.

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