Question

Fill in the blank to form a correct inequality statement. If \(3 x=12,\) then \(x______4\)

Short answer

x = 4

Step-by-step solution

Isolate the Variable

First, solve the equation given: \(3x = 12\). To isolate \(x\), divide both sides of the equation by 3.

Simplify the Equation

After dividing both sides by 3, we get: \(x = \frac{12}{3}\). This simplifies to \(x = 4\).

Form the Inequality

Given that \(x\) equals 4, we must choose the suitable inequality symbol to fill in the blank. Since \(x = 4\) is neither greater than nor less than 4, the correct inequality symbol is \(=\).

Key concepts

solving equations

Let’s understand how to solve equations. Solving an equation means finding the value of the variable that makes the equation true. Look at the equation provided: \(3x = 12\).
To solve it, we need to perform operations that will isolate the variable on one side of the equation.

isolation of variables

The key to solving an equation is isolating the variable. Here, we need to isolate \(x\) from the equation \(3x = 12\).

• Divide both sides of the equation by the coefficient of \(x\), which is 3.
• When we divide, we get \(x = \frac{12}{3}\).

This step brings us closer to finding the value of \(x\).

simplifying expressions

After isolating \(x\), the next step is simplification. Simplifying means making the expression as simple as possible. Here, we simplify \(x = \frac{12}{3}\) to get \(x = 4\).

• It is essential to simplify to get the most straightforward answer.
• With \(x = 4\), we then form our inequality statement, \(x = 4\).

This method shows how isolating and simplifying help solve equations efficiently.