Answer:
[tex]\boxed {\boxed {\sf y= -1.2 }}[/tex]
Step-by-step explanation:
We are asked to solve the following equation for y.
[tex]-2y-4.2= 1.8 + 3y[/tex]
To solve for y, we have to isolate the variable by performing the inverse operations. First, move all the terms without a variable or the constants to one side, and the terms with a variable to the other side.
4.2 is being subtracted and the inverse operation of subtraction is addition. Add 4.2 to both sides.
[tex]-2y-4.2 +4.2= 1.8 + 3y+ 4.2[/tex]
[tex]-2y=1.8 + 4.2 + 3y[/tex]
[tex]-2y= 6 + 3y[/tex]
3y is being added and the inverse operation of addition is subtraction. Subtract 3y from both sides.
[tex]-2y-3y= 6+ 3y -3y[/tex]
[tex]-2y-3y= 6[/tex]
[tex]-5y=6[/tex]
y is being multiplied by -5. The inverse operation of multiplication is division. Divide both sides by -5.
[tex]\frac {-5y}{-5}= \frac{6}{-5}[/tex]
[tex]y=- 1.2[/tex]
Check the answer by substituting -1.2 back into the original equation.
[tex]-2 (-1.2)-4.2 = 1.8 + 3(-1.2)[/tex]
[tex]2.4-4.2=1.8 + - 3.6[/tex]
[tex]-1.8 = -1.8[/tex]
This checks out, so we know our answer is correct.
