91Ó°ÊÓ

In the world of algebra, solving for a variable means finding the value of the variable that makes the equation true. Imagine the variable, like \(x\), as a box you need to uncover to see what's inside.
When dealing with an equation like

• -1.7 = 1.2 - x

we want to rearrange it until \(x\) is standing alone on one side of the equality sign. This process involves manipulating the equation by performing the same operations on both sides. The goal is to gradually peel away numbers and other terms so that \(x\) is isolated.
For instance, we first subtracted \(1.2\) from both sides to begin unraveling \(x\). The subtraction handed us a simpler expression:

• -2.9 = -x

From there, a quick multiplication by \(-1\) provided the answer:

• x = 2.9

Once you've solved for the variable, it's vital to ensure your solution is correct. This step is like double-checking your homework before turning it in.
Substitute your solution for the variable back into the original equation. In our example:

• Start with -1.7 = 1.2 - x

If we've determined \(x\) is \(2.9\), substitute this value in place of \(x\):

• -1.7 = 1.2 - 2.9

Then, calculate the right-hand side:

• 1.2 - 2.9 = -1.7

If both sides of the equation are equal, then the solution \(x = 2.9\) is indeed correct. This validation step forms a crucial part of solving algebraic equations as it eliminates errors and secures confidence in your answer.

Equation isolation simply means getting the variable you want to solve for by itself on one side of the equation. This makes it easier to interpret its value.
To achieve this with the equation

• -1.7 = 1.2 - x

start by focusing on moving terms so that \(x\) ends up isolated. This might require several operations: addition, subtraction, multiplication, or division. Let’s walk through the process:
First, subtract \(1.2\) from both sides to remove the number associated with \(x\):

• -2.9 = -x

The goal is to transform this into an equation that's simple to solve. Finally, multiply both sides by \(-1\):

• x = 2.9

After isolating \(x\), the problem becomes straightforward to solve. It's like giving directions where the final destination is reached with clarity.