What is the solution to this equation? 3x – 7 + 4x = 28 A. x = 35 B. x = 5 C. x = 21 D. x = 3
The correct answer and explanation is:
Correct Answer: B. x = 5
To solve the equation 3x−7+4x=283x – 7 + 4x = 28, start by combining like terms. The terms 3x3x and 4x4x are both variable terms that can be added together. When added, they become 7x7x. This reduces the equation to:
7x−7=287x – 7 = 28
Next, isolate the term with the variable by eliminating the constant term on the left side. To remove the -7, add 7 to both sides of the equation:
7x−7+7=28+77x – 7 + 7 = 28 + 7
This simplifies to:
7x=357x = 35
At this point, only the multiplication remains. To isolate xx, divide both sides of the equation by 7:
7×7=357\frac{7x}{7} = \frac{35}{7}
So, the solution is:
x=5x = 5
Double-checking the solution by substituting x=5x = 5 back into the original equation ensures accuracy. Substituting gives:
3(5)−7+4(5)=283(5) – 7 + 4(5) = 28
Calculating step by step:
15−7+20=2815 – 7 + 20 = 28
28=2828 = 28
The left side equals the right side, confirming that the solution is correct.
Solving linear equations like this demonstrates the fundamental concept of balancing both sides using inverse operations. Each step uses basic arithmetic rules: combining like terms, adding or subtracting the same value on both sides, and dividing or multiplying by the coefficient of the variable. These steps maintain the equality of the equation while isolating the variable. Mastering this process is important in algebra because it serves as a foundation for solving more complex equations involving multiple steps, fractions, or parentheses. By following each step carefully, any linear equation with one variable can be solved systematically.