Algebra

3 ( 2 x − 5 ) + 4 = 2 ( x + 7 )

Step-by-step solution with explanation

Final Answer

Step-by-step solution

1

Write the original equation clearly

We start by writing the equation so we can see exactly what we need to solve. Our goal is to find the value of x.
2

Distribute on both sides

Multiply 3 by each term inside the first set of parentheses: 3·2x = 6x and 3·5 = 15. Multiply 2 by each term inside the second set: 2·x = 2x and 2·7 = 14.
3

Combine like terms on the left

On the left side, combine the constants: -15 + 4 = -11. The right side stays the same.
4

Move x terms to one side

Subtract 2x from both sides so all the x terms are on the left. This keeps the equation balanced.
5

Simplify the x terms

6x - 2x = 4x. Now we have a simple two-step equation to finish solving.
6

Add 11 to both sides

Adding 11 to both sides cancels out the -11 on the left, isolating the term with x.
7

Divide both sides by 4

Dividing both sides by 4 gives us x by itself. 25 ÷ 4 = 6.25, which can also be written as the fraction 25/4.

Understanding this problem

Learning Insight

This is a linear equation, meaning x appears only to the first power. Linear equations always have exactly one solution. The key idea is to use opposite operations — like adding to undo subtracting — to peel away everything around x until it stands alone.

Quick Tip

After distributing, quickly combine all constants and all x-terms on each side before moving anything across the equals sign. It keeps your work neat and cuts down on errors.

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 — the 3 must multiply both 2x AND -5.