Question

Solve the algebraic equation: 3(x−2)+2=4x−5.

Answer 1

To solve the algebraic equation 3(x−2)+2=4x−5, distribute the 3 to both terms inside the parentheses, combine like terms, isolate the variable, and solve for x. The solution is x = 1.

Step-by-step explanation:

To solve the algebraic equation 3(x−2)+2=4x−5, we need to apply the distributive property and combine like terms. Here are the steps:

1. Distribute the 3 to both terms inside the parentheses: 3(x-2) = 3x - 6.
2. Combine like terms on the left side: 3x - 6 + 2 = 4x - 5.
3. Add 6 to both sides to isolate the variable on one side: 3x - 6 + 2 + 6 = 4x - 5 + 6.
4. Combine like terms on the left side: 3x + 2 = 4x + 1.
5. Subtract 3x from both sides to isolate the variable: 3x - 3x + 2 = 4x - 3x + 1.
6. Combine like terms on the left side: 2 = x + 1.
7. Subtract 1 from both sides to solve for x: 2 - 1 = x + 1 - 1.
8. Simplify: 1 = x.

So, the solution to the equation is x = 1.