Solve for y.
–5y – 9 = –(y – 1)
a) - 1/2
b) - 2 1/2
c) -2
d) - 2/5
Starting with –5y – 9 = –(y – 1), we can distribute the negative sign on the right side:
–5y – 9 = –y + 1.
Now let's combine like terms by adding y to both sides:
–4y – 9 = 1.
Next, let's isolate the variable term by adding 9 to both sides:
–4y = 10.
Finally, we solve for y by dividing both sides by –4:
y = -10/4 = -5/2 = -2 1/2.
Therefore, the solution is b) - 2 1/2.
To solve for y, we will first simplify the equation step by step.
Step 1: Distribute the negative sign to both terms on the right side of the equation:
-5y - 9 = -y + 1
Step 2: Move all terms containing y to one side of the equation by adding y to both sides:
-5y + y - 9 = -y + y + 1
This simplifies to:
-4y - 9 = 1
Step 3: Move the constant term (-9) to the other side of the equation by adding 9 to both sides:
-4y - 9 + 9 = 1 + 9
This simplifies to:
-4y = 10
Step 4: Divide both sides of the equation by -4 to solve for y:
(-4y) / (-4) = 10 / (-4)
This simplifies to:
y = -10 / 4
Step 5: Simplify the fraction:
y = -5 / 2
Therefore, the solution for y is -5 / 2, which is equivalent to -2 1/2. The correct option is b) - 2 1/2.