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QuestionSolve the equation: 3.92y−7.72y−5.67=3.033.92y - 7.72y - 5.67 = 3.03. Provide your answer as an integer, fraction, or rounded decimal.

Studdy Solution

STEP 1

Assumptions1. The equation given is 3.92y−7.72y−5.67=3.033.92y -7.72y -5.67 =3.03 . The variable to solve for is yy
3. The solution should be expressed as an integer, simplified fraction, or decimal rounded to two decimal places

STEP 2

First, we need to simplify the left side of the equation by combining like terms.
.92y−7.72y−5.67=.03.92y -7.72y -5.67 =.03

STEP 3

Combine the terms with yy.
(−7.72+3.92)y−5.67=3.03(-7.72 +3.92)y -5.67 =3.03

STEP 4

Calculate the coefficient of yy.
(−3.8)y−.67=3.03(-3.8)y -.67 =3.03

STEP 5

Next, we need to isolate the term with yy on one side of the equation. We can do this by adding 5.675.67 to both sides.
(−3.8)y−5.67+5.67=3.03+5.67(-3.8)y -5.67 +5.67 =3.03 +5.67

STEP 6

implify both sides of the equation.
(−3.8)y=8.(-3.8)y =8.

STEP 7

To solve for yy, we need to divide both sides of the equation by the coefficient of yy, which is −3.-3..
y=.7−3.y = \frac{.7}{-3.}

STEP 8

Calculate the value of yy.
y=−2.28947y = -2.28947

STEP 9

Since the problem asks for the solution to be expressed as an integer, simplified fraction, or decimal rounded to two decimal places, we round the solution to two decimal places.
y=−2.29y = -2.29So, the solution to the equation 3.92y−7.72y−5.67=3.033.92y -7.72y -5.67 =3.03 is y=−2.29y = -2.29.

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