Question

Solve the equation. $$ 3(r-1)=2(r-2) $$

Short answer

The solution of the equation \(3(r-1) = 2(r-2)\) is \(r = -1\)

Step-by-step solution

Simplify on both sides

To get started, first simplification is essential. By using distributive property (which means a(b+c) = ab + ac), Simplify both sides of the equation. So, multiply \(3\) through the parentheses on the left side and \(2\) on the right side of the equal sign: \(3r - 3 = 2r - 4\)

Rearrange the equation

Next step is to make one side of the equation a variable term and another side as numerical term. To do this, subtract \(2r\) from both sides and then add \(3\) to both sides of the equation: \(3r - 2r = -4 + 3\), so we get \(r = -1\)

Check the solution

The final step is to check their solution to make sure it's correct. Substitute \(r = -1\) into the original equation and see if it verifies the equation: \(3(-1-1)=2(-1-2)\). If the left side of the equation equals to the right side, then the solution is correct, and indeed in this case, \(-6 = -6\), thus solution is confirmed