91Ó°ÊÓ

A first-degree equation is one of the simplest types of linear equations, where the variable is raised to the power of one. These equations typically involve operations of addition, subtraction, multiplication, or division, and the overall goal is to solve for the variable. The general form of a first-degree equation is \(ax + b = c\), where \(x\) is the variable, and \(a\), \(b\), and \(c\) are constants. In our problem, the equation presented is \(29 = \frac{x}{4}\). Here, the variable \(x\) is divided by 4, and we need to rearrange it to solve for \(x\). First-degree equations are fundamental as they form the basis for understanding more complex algebraic concepts. Breaking them down helps in tackling more involved equations later.

The key to solving any equation involving a variable is to isolate that variable. This means rearranging the equation such that the variable stands alone on one side. In the equation \(29 = \frac{x}{4}\), our mission is to isolate \(x\). Currently, it is trapped inside a fraction, with 4 as the denominator.
To free \(x\), we need to perform the opposite operation of what is being done to it. Thus, we multiply both sides of the equation by 4, yielding \(4 \times 29 = x\).
By applying multiplication, we have effectively isolated \(x\). This operation maintains equality because if you perform an action on one side, you must also perform it on the other. Now, \(x\) is isolated, allowing us to easily compute its value.

The multiplication property of equality states that if you multiply both sides of an equation by the same number, the two sides remain equal. This property is crucial for maintaining the balance of the equation when manipulating it to solve for a variable.
In our exercise, we applied this principle to the equation \(29 = \frac{x}{4}\). By multiplying both sides by 4, we eliminate the fraction and simplify the equation to \(116 = x\).
Using multiplication this way helps normalize the equation, making the variable calculation straightforward. Remember: whatever you do to one side of the equation, you must do to the other to keep the equation valid. This is analogous to keeping a scale balanced – every action has an equal counteraction on the opposite side. Understanding this concept ensures that your algebraic solutions are correct every time.