91Ó°ÊÓ

When solving linear equations, our goal is to find the value of the unknown variable. To achieve this, we need to isolate the variable. In the given problem, we start with the equation: \( -3.1x - 2 = -29.9 \). The first step is to move any constants (numbers without variables) to the other side of the equation. We do this by performing operations that will cancel out the constants on the variable's side.

In the given equation, we have \( -3.1x - 2 \). To isolate the term with x, we need to remove -2. We do this by adding 2 to both sides of the equation because adding a number and its opposite will cancel out to zero:

\( -3.1x - 2 + 2 = -29.9 + 2 \).
This simplifies to:
\( -3.1x = -27.9 \).

Now, the variable term is isolated on one side of the equation, setting us up for the next step.

Simplifying equations is about making the problem more manageable. After isolating the variable term, the equation often needs simplifying by performing arithmetic operations. In our example, we've already transformed the original equation to \( -3.1x = -27.9 \). Simplification means we've made the equation less complex and ready for the final solving steps.

Remember, simplifying can involve:

• Combining like terms
• Performing arithmetic operations
• Eliminating fractions or decimals if necessary

Simplification often makes the equation clearer and easier to solve.

In this problem, since there are no further terms to combine or simplify, we proceed with solving for the variable.

The final step in solving our equation \( -3.1x = -27.9 \) involves using division. When you have an equation of the form \( ax = b \), you solve for x by dividing both sides of the equation by the coefficient of x, which is a.

In our case, the coefficient is -3.1. We divide both sides by -3.1 to find the value of x:

\( \frac{-3.1x}{-3.1} = \frac{-27.9}{-3.1} \).

This reduces to:
\( x = 9 \).

Performing division in equations is crucial because it allows us to directly find the value of the variable. For division:

• Make sure you're dividing both sides by the exact same number
• Keep track of the sign (positive or negative)

So in summary, by dividing -27.9 by -3.1, we isolate x and solve the equation successfully. The solution is \( x = 9 \).