1). 5 - (t + 3) = -1 + 2(t - 3)
5 - (t + 3) = -1 + 2(t - 3)
5 - t + 3 = -1 + 2t - 6
2 + 7 = 3t
3 = t
How does the second number become a 7?
-1 + -6 = -7
Add 7 to both sides of the equation.
To solve the equation 5 - (t + 3) = -1 + 2(t - 3), we will simplify both sides of the equation.
First, let's simplify the left side: 5 - (t + 3).
We can start by removing the parentheses using the distributive property. When we distribute the negative sign, it changes the sign of every term inside the parentheses. So, we have:
5 - t - 3.
Simplifying further, we combine like terms: -t - 3.
Now, let's simplify the right side of the equation: -1 + 2(t - 3).
Again, we can distribute the 2 to each term within the parentheses: 2t - 6.
So, the right side becomes:
-1 + 2t - 6.
Combining like terms, we have: 2t - 7.
Now, the equation becomes: 5 - t - 3 = -1 + 2t - 6.
Next, let's combine like terms on both sides of the equation:
(5 - 3) - t = (-1 - 6) + 2t.
Simplifying further, we have:
2 - t = -7 + 2t.
Now, let's isolate the variables on one side and constants on the other side.
First, let's get rid of the -t on the left side by adding t to both sides of the equation:
2 - t + t = -7 + 2t + t.
Simplifying the left side by cancelling out -t and +t, we have:
2 = -7 + 3t.
Next, let's isolate the constant term on the right side by subtracting -7 from both sides:
2 + 7 = -7 + 3t + 7.
Simplifying the right side by cancelling out -7 and +7, we have:
9 = 3t.
Finally, we solve for t by dividing both sides of the equation by 3:
9/3 = 3t/3.
Simplifying, we get:
3 = t.
So, the solution to the equation 5 - (t + 3) = -1 + 2(t - 3) is t = 3.