Which steps can be used in order to determine the solution to $-1.3+4.6 x=0.3+4 x$?

A. Subtract 1.3 from both sides of the equation, add $4 x$ to both sides of the equation, then divide by the coefficient of $x$.
B. Subtract 1.3 from both sides of the equation, subtract $4.6 x$ from both sides of the equation, then divide both sides by the coefficient of $x$.
C. Add 1.3 to both sides of the equation, subtract $4.6 x$ from both sides of the equation, then divide both sides by the coefficient of $x$.
D. Add 1.3 to both sides of the equation, subtract $4 x$ from both sides of the equation, then divide both sides by the coefficient of $x$.

To solve the equation − 1.3 + 4.6 x = 0.3 + 4 x , the correct steps are to add 1.3 to both sides, subtract 4 x , and then divide by the coefficient of x , leading to x = 3 8 ​ . Therefore, the chosen option is D .
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Answered by Anonymous | 2025-07-04

Add 1.3 to both sides of the equation: − 1.3 + 4.6 x + 1.3 = 0.3 + 4 x + 1.3 , which simplifies to 4.6 x = 4 x + 1.6 .
Subtract 4 x from both sides of the equation: 4.6 x − 4 x = 4 x + 1.6 − 4 x , which simplifies to 0.6 x = 1.6 .
Divide both sides of the equation by the coefficient of x : 0.6 0.6 x ​ = 0.6 1.6 ​ , which simplifies to x = 3 8 ​ .
The correct steps are: Add 1.3 to both sides of the equation, subtract 4 x from both sides of the equation, then divide both sides by the coefficient of x .

Explanation

Analyzing the Problem We are given the equation − 1.3 + 4.6 x = 0.3 + 4 x and asked to identify the correct steps to solve for x . We will analyze each option to determine which one correctly isolates x .

Analyzing Option 1 Let's analyze the first option: Subtract 1.3 from both sides, add 4 x to both sides, then divide by the coefficient of x .

Subtract 1.3 from both sides: − 1.3 + 4.6 x − 1.3 = 0.3 + 4 x − 1.3 , which simplifies to 4.6 x − 2.6 = 4 x − 1 .

Add 4 x to both sides: 4.6 x − 2.6 + 4 x = 4 x − 1 + 4 x , which simplifies to 8.6 x − 2.6 = 8 x − 1 . This does not isolate x effectively, so this option is incorrect.

Analyzing Option 2 Let's analyze the second option: Subtract 1.3 from both sides, subtract 4.6 x from both sides, then divide by the coefficient of x .

Subtract 1.3 from both sides: − 1.3 + 4.6 x − 1.3 = 0.3 + 4 x − 1.3 , which simplifies to 4.6 x − 2.6 = 4 x − 1 .

Subtract 4.6 x from both sides: 4.6 x − 2.6 − 4.6 x = 4 x − 1 − 4.6 x , which simplifies to − 2.6 = − 0.6 x − 1 .

Divide both sides by the coefficient of x : − 0.6 − 2.6 ​ = − 0.6 − 0.6 x − 1 ​ , which simplifies to 3 13 ​ = x + 3 5 ​ . This is not the most direct way to solve for x , but it is a valid approach.

Analyzing Option 3 Let's analyze the third option: Add 1.3 to both sides, subtract 4.6 x from both sides, then divide by the coefficient of x .

Add 1.3 to both sides: − 1.3 + 4.6 x + 1.3 = 0.3 + 4 x + 1.3 , which simplifies to 4.6 x = 4 x + 1.6 .

Subtract 4.6 x from both sides: 4.6 x − 4.6 x = 4 x + 1.6 − 4.6 x , which simplifies to 0 = − 0.6 x + 1.6 .

Divide both sides by the coefficient of x : − 0.6 0 ​ = − 0.6 − 0.6 x + 1.6 ​ , which simplifies to 0 = x − 3 8 ​ . This is a valid approach.

Analyzing Option 4 Let's analyze the fourth option: Add 1.3 to both sides, subtract 4 x from both sides, then divide by the coefficient of x .

Add 1.3 to both sides: − 1.3 + 4.6 x + 1.3 = 0.3 + 4 x + 1.3 , which simplifies to 4.6 x = 4 x + 1.6 .

Subtract 4 x from both sides: 4.6 x − 4 x = 4 x + 1.6 − 4 x , which simplifies to 0.6 x = 1.6 .

Divide both sides by the coefficient of x : 0.6 0.6 x ​ = 0.6 1.6 ​ , which simplifies to x = 3 8 ​ . This is the most direct and efficient approach.

Determining the Correct Option Comparing the options, the fourth option provides the most straightforward steps to solve for x .


Examples
When solving linear equations in physics, such as determining the position of an object moving at a constant velocity, you often need to isolate a variable. The steps of adding constants to both sides and subtracting variables from both sides are fundamental in these calculations. For example, if you have the equation d = v × t + d 0 ​ , where d is the final distance, v is the velocity, t is the time, and d 0 ​ is the initial distance, you can isolate t by first subtracting d 0 ​ from both sides and then dividing by v . This process is analogous to the algebraic manipulations used in the given problem.

Answered by GinnyAnswer | 2025-07-04