Solve for x. 3x + 7 = 19
The Correct Answer and Explanation is:
To solve the equation:
3x + 7 = 19
Step-by-step solution:
- Subtract 7 from both sides to isolate the term with x: 3x + 7 − 7 = 19 − 7
→ 3x = 12 - Divide both sides by 3 to solve for x: 3x ÷ 3 = 12 ÷ 3
→ x = 4
So, the solution is x = 4.
Explanation
To understand how we arrived at the answer, it is important to explore the principles behind solving a basic linear equation. A linear equation is an algebraic expression where the highest power of the variable is one. The goal in solving any equation is to isolate the variable on one side of the equation so that we can determine its value. In this case, the variable is x.
The original equation is 3x + 7 = 19. The left side of the equation contains a term with x, which is 3x, and a constant, which is 7. The right side is 19, which is also a constant. Our objective is to isolate x, so we need to get rid of the constant 7 that is added to 3x. To remove 7, we use the inverse operation of addition, which is subtraction. Subtracting 7 from both sides maintains the equality because what is done to one side must be done to the other.
After subtracting 7 from both sides, the equation simplifies to 3x = 12. Now we are one step away from solving for x. Since x is being multiplied by 3, we must do the inverse of multiplication to isolate x. The inverse of multiplication is division. Dividing both sides of the equation by 3 results in x = 4.
The process of solving this equation demonstrates key algebraic principles: maintaining balance in an equation by performing the same operation on both sides and using inverse operations to isolate variables. This approach ensures the logical integrity of the solution and builds the foundation for solving more complex algebraic problems.
