5(x-3)-3(x-1)
5(x-3)-3(x-1)
5x - 15 - 3x + 1
2x - 14
5(x-3)-3(x-1)
5x - 15 - 3x + 3
2x - 12
To simplify the expression 5(x-3)-3(x-1), we need to apply the distributive property and then combine like terms.
Step 1: Distributive Property
Multiply each term inside the parentheses by the coefficient outside.
For the first set of parentheses, (x-3), the coefficient outside is 5:
5(x-3) = 5*x - 5*3 = 5x - 15
For the second set of parentheses, (x-1), the coefficient outside is 3:
-3(x-1) = -3*x + (-3)*(-1) = -3x + 3
Now our expression becomes:
5x - 15 - 3x + 3
Step 2: Combine Like Terms
Combine the x terms and the constant terms separately:
For the x terms, we have 5x and -3x. Combining them gives:
5x - 3x = 2x
For the constant terms, we have -15 and +3. Combining them gives:
-15 + 3 = -12
Putting it all together, our simplified expression is:
2x - 12
So, 5(x-3) - 3(x-1) simplifies to 2x - 12.