91Ó°ÊÓ

The first step in solving a linear equation is to isolate the variable. This means getting the variable (in this case, x) by itself on one side of the equation. In our example, the equation is given as:$$0.6x = -1.44.$$To isolate x, we need to get rid of the coefficient 0.6 multiplying it. The simplest way to do this is by performing the opposite operation. Since 0.6 is multiplied by x, we divide both sides of the equation by 0.6:$$x = \frac{-1.44}{0.6}.$$By dividing both sides by 0.6, we effectively isolate x, leaving it alone on the left-hand side of the equation. This step is crucial because it transforms the equation into a simpler form where we can directly solve for the variable.

Once the variable is isolated, the next step is to simplify the resulting expression. In our example, after isolating x, we obtain:$$x = \frac{-1.44}{0.6}.$$The goal here is to simplify the right-hand side of the equation by performing the division. Calculating this division gives us:$$x = -2.4.$$Simplifying expressions often involves performing basic arithmetic operations like addition, subtraction, multiplication, and division. Always make sure to perform these operations accurately to avoid mistakes in the final solution. In this case, dividing -1.44 by 0.6 gives us the simplified value of -2.4 for x.

After finding the solution, it is important to verify that our answer is correct. This can be done by substituting the solution back into the original equation and checking if both sides are equal. In our example, we calculated that x = -2.4. To verify this, we substitute -2.4 for x in the original equation:$$0.6(-2.4) = -1.44.$$Next, we perform the multiplication on the left-hand side:$$0.6 \times -2.4 = -1.44.$$Since both sides of the equation are equal, our solution is verified to be correct. Verifying solutions ensures that our method and calculations are accurate, and it helps confirm that the solution satisfies the original problem statement.