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what is-4y-(5y+6)=-7y+3

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3 Answers

     -4y - (5y + 6) = -7y + 3

Distribute the negative sign into the terms inside the parentheses on the left hand side:

     -4y + (-5y - 6) = -7y + 3

     -4y + -5y + -6 = -7y + 3

     -4y - 5y - 6 = -7y + 3

Combine like terms in left hand side of equation:

     -9y - 6 = -7y + 3

Isolate the unknown variable (y) to one side of the equation by adding 7y to both sides of equation then adding 6 to both sides of the equation:

     -9y + 7y - 6 = -7y + 7y + 3

     -2y - 6 = 3

     -2y - 6 + 6 = 3 + 6

     -2y = 9

Divide both sides by -2 to solve for y:

     -2y/-2 = 9/-2

     y = -9/2 

Hi Courtney!  I see that you have an equation of -4y-(5y+6)=-7y+3.  Here's how you solve it:

1.  Use the acronym PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction).

2.  Ask yourself about each of these operations to show your work like this:

-4y-(5y+6)=-7y+3                                    Parentheses, yet everything is already simplified.

-4y-1*(5y+6)=-4y-1*5y-1*6=-7y+3          Distributive property

-4y-5y-6=-7y+3                                       Multiplication

-9y-6=-7y+3                                            Combine like terms and simplify.

+7y+6=+7y+6                                         Add whatever you want to both sides of the equation.

-2y     =      9                                           Final equation.

-2y/-2   =     9/-2                                     Divide each side of the equation by 2.

y   =     -4.5                                            Here is the solution for y.

 

Now to check the solution, since we have found the value for y, we should plug it into the equation to see if it is right.

-4*-4.5-(5*-4.5+6)=-7*-4.5+3

-4*-4.5-(-22.5+6)=-7*-4.5+3

-4*-4.5-(-16.5)=-7*-4.5+3

18-1*-16.5=31.5+3

18+16.5=31.5+3

34.5=34.5             Check!

Hi, Courtney!

First, you need to get rid of parentheses. Remember, if there is a minus sign in front of the opening parenthesis, all signs of the terms inside the parentheses have to be changed into opposite ones. In this case, left-hand side is transformed as follows:

-4y-(5y+6)=-4y-5y-6. Now we obtained the following equation:

-4y-5y-6=-7y+3

Let us now collect terms containing y on one side (right) and pure numbers on the other side (left). The rule is that you can move any term into the opposite side of equation if you change its sign. In this case, let us first move -7y from the right to the left side. We first change -7y into 7y and write it on the left side instead of right side.

-4y-5y+7y-6=3.

Next step, move -6 into the right side. We again change its sign to have 6 instead of -6 and move it to the right side. We will get:

-4y-5y+7y=3+6

Now let us collect like terms. It is easy on the right side, there 3+6 is simply 9. On the left side, y is a common factor, we can factor it out to get (-4-5+7)y. Now if you add everything in parentheses up, you will get -2. So the equation is simplified to the following: (-2)y=9. This shall be easy to solve now. Divide both sides by -2 to get rid of the coefficient in front of y and obtain a solution: (-2)y/(-2)=9/(-2) or y=-4.5

So the answer is y=-4.5.