Solving the Linear Equation \(x - 4 = -3\)

To find the value of the variable \(x\) in the equation \(x - 4 = -3\), we need to isolate \(x\) on one side of the equals sign.

The equation we need to solve is:

\(x - 4 = -3\)

We can get \(x\) by itself by performing the opposite operation of subtracting 4, which is adding 4. To keep the equation balanced, we must perform this operation on both sides of the equals sign.

Add 4 to both sides of the equation:

\(x - 4 + 4 = -3 + 4\)

Now, simplify both sides of the equation:

On the left side, \(x - 4 + 4\) simplifies to \(x\).

On the right side, \(-3 + 4\) simplifies to \(1\).

So, the equation becomes:

\(x = 1\)

Thus, the solution to the equation \(x - 4 = -3\) is \(x = 1\).

Let's look at the given options to see which one matches our solution:

• Option A: 7
• Option B: -1
• Option C: -7
• Option D: 1

Our calculated value for \(x\), which is 1, matches Option D.

Revision Table: Key Steps to Solve Linear Equations

Additional Information: Basics of Linear Equations

A linear equation is an equation where the variable (like \(x\)) has an exponent of 1. The graph of a linear equation in two variables is a straight line.

Simple linear equations in one variable, like \(x - 4 = -3\), involve finding a single numerical value for the variable that makes the equation true.

To solve these equations, we use the principle that whatever operation is done to one side of the equation must also be done to the other side to maintain the equality. Common inverse operations include:

• Addition is the inverse of subtraction.
• Multiplication is the inverse of division.

By applying inverse operations, we can move terms around and isolate the variable to find its value.