Algebra

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

Step-by-step solution with explanation

Final Answer

Step-by-step solution

1

Distribute 3 on the left side

Multiply 3 by each term inside the parentheses. 3 times 2x is 6x, and 3 times -5 is -15.
2

Distribute 2 on the right side

Multiply 2 by each term inside the parentheses. 2 times x is 2x, and 2 times 7 is 14.
3

Combine like terms on the left

-15 + 4 equals -11, so we simplify the left side to 6x - 11.
4

Move variable terms to the left

Subtract 2x from both sides to get all x terms on the left side.
5

Isolate the variable x

Add 11 to both sides to move the constant to the right side.
6

Solve for x by dividing

Divide both sides by 4 to get x by itself. 25 divided by 4 is 6.25.

Understanding this problem

Learning Insight

This is a linear equation, meaning x has no exponents. Linear equations always have exactly one solution. The process — distribute, combine like terms, isolate x — is the core strategy for solving any linear equation.

Quick Tip

After solving, plug your answer back in to check: 3(2(6.25) - 5) + 4 = 3(7.5) + 4 = 26.5, and 2(6.25 + 7) = 2(13.25) = 26.5 ✓

Common Mistake

Students often forget to distribute the number outside the parentheses to EVERY term inside. For example, writing 3(2x - 5) as 6x - 5 instead of 6x - 15.