Solve.
3p-1=5(p-1)-2(7-2p)
3p-1 = 5p - 5 - 14 +4p
18 = 6p
3 = p
To solve the equation 3p - 1 = 5(p - 1) - 2(7 - 2p), we need to apply the distributive property and simplify both sides of the equation.
First, distribute the terms on the right side by multiplying:
3p - 1 = 5p - 5 - 2 * 7 + 2 * 2p
Now simplify each side:
3p - 1 = 5p - 5 - 14 + 4p
Combine like terms:
3p - 1 = 9p - 19
To continue solving the equation, let's isolate the variable p on one side of the equation. We can do this by moving the terms involving p to one side and the constant terms to the other side.
Subtract 3p from both sides:
3p - 3p - 1 = 9p - 3p - 19
Simplify:
-1 = 6p - 19
Next, add 19 to both sides:
-1 + 19 = 6p - 19 + 19
Simplify:
18 = 6p
Finally, divide both sides by 6 to solve for p:
18/6 = 6p/6
Simplify:
3 = p
Therefore, the solution to the equation 3p - 1 = 5(p - 1) - 2(7 - 2p) is p = 3.