Algebra

3(2x - 5) + 4 = 2(x + 7) + 3x

Step-by-step solution with explanation

Final Answer

Step-by-step solution

1

Distribute on the left side

Multiply 3 by each term inside the parentheses. 3 times 2x is 6x, and 3 times -5 is -15. The +4 stays as is.
2

Simplify the left side

Combine the constants on the left: -15 + 4 = -11. So the left side becomes 6x - 11.
3

Distribute on the right side

Multiply 2 by each term inside the parentheses. 2 times x is 2x, and 2 times 7 is 14. The +3x stays as is.
4

Simplify the right side

Combine like terms on the right: 2x + 3x = 5x. So the right side becomes 5x + 14.
5

Set simplified sides equal, move x terms

Subtract 5x from both sides to get all x terms on the left. Then add 11 to both sides to move the constant to the right.
6

Solve for x

6x - 5x = x, and 14 + 11 = 25. So x = 25. This is the one and only solution.

Understanding this problem

Learning Insight

This is a linear equation — the variable x has no exponents, so there is exactly one solution. When you simplify both sides and move all x terms together, you always end up with something like 1x = number, giving a single answer.

Quick Tip

Always distribute first, then combine like terms on each side before moving anything across the equals sign. Doing it in that order prevents most arithmetic errors.

Common Mistake

Students often forget to distribute the negative sign or multiply EVERY term inside the parentheses. For example, writing 3(2x - 5) as 6x - 5 instead of 6x - 15 is one of the most common errors here.