Problem 51 - Algebra A Combined Function

Question

\(4.4=-0.8 x\)

Step-by-Step Solution

Answer

x = -5.5

Step 1: Identify the Equation

The given equation is \(4.4 = -0.8x\). We need to solve for \(x\).

Step 2: Isolate the Variable

To find \(x\), we must isolate it. We do this by dividing both sides of the equation by \(-0.8\) to cancel out the coefficient of \(x\). This gives us \(x = \frac{4.4}{-0.8}\).

Step 3: Perform the Division

Now, we calculate \(\frac{4.4}{-0.8}\). Dividing 4.4 by -0.8 gives us \(-5.5\). Therefore, \(x = -5.5\).

Key Concepts

Algebra

Algebra is a branch of mathematics that uses letters and symbols to represent numbers and quantities in formulas and equations. It provides a way to describe relationships between variables and constants. In algebra, we often solve equations, like the given equation, to find the value of the unknown variable.

Understanding basic algebraic operations is key to solving these problems. You will use operations like addition, subtraction, multiplication, and division to manipulate equations. The goal is to simplify these equations and find the value of the unknown variable.

• Variables: These are symbols that stand for numbers that haven't been determined yet. In the equation, "\(x\)" is our variable.
• Constants: These are numbers that are already known and do not change. "4.4" and "-0.8" are constants in our example.

Knowing how to structure these elements is essential in solving algebraic equations effectively, as seen in our original exercise.

Isolating the Variable

A crucial step in solving any equation is to isolate the variable. This means rearranging the equation so that the variable is on one side and everything else is on the other. By doing this, we find out what the variable equals.

To isolate a variable, you can use the inverse operations of what is being done to the variable. For multiplication, you'd use division, and vice versa. In the example, "\(-0.8x\)" means \(-0.8\) is multiplied by \(x\). To isolate \(x\), you divide both sides of the equation by \(-0.8\).

Here's a quick checklist for isolating the variable:

• Look for the operation performed on the variable.
• Apply the inverse operation to both sides of the equation.
• Continue until the variable is by itself.

Following these steps will help you solve for the unknown and make the equation easy to understand.

Division in Equations

Division is often used in algebra to cancel out coefficients of variables. When you have an equation like "\(4.4 = -0.8x\)", you use division to solve for "\(x\)". Here's how it works:

• Identify the coefficient (the number multiplying the variable).
• Divide both sides of the equation by this coefficient.
• Simplify the division on both sides to solve for the variable.

In our equation, dividing 4.4 by \(-0.8\) gives \(-5.5\), isolating \(x\). Remember, dividing by a negative number switches the sign of the result. This key step in solving equations ensures that you accurately find the variable's value. By mastering division in equations, you simplify algebraic expressions and effectively solve equations, making algebra much easier to tackle.