How to Solve Linear Equations: Step-by-Step Guide
Quick Answer
To solve the equation F - 1 - 2F = -2 × 3 + F, first simplify both sides and combine like terms. You will find that F = 2.5.
Solving linear equations is a fundamental skill in mathematics that helps students understand how to manipulate expressions and isolate variables. In this guide, we will break down the steps to solve the equation F - 1 - 2F = -2 × 3 + F.
**Step 1: Simplify the Equation**
The first task is to simplify both sides of the equation. Begin with the right side:
-2 × 3 equals -6.
Now, rewrite the equation:
F - 1 - 2F = -6 + F.
**Step 2: Combine Like Terms**
Next, let's combine like terms. On the left side, F and -2F can be combined:
F - 2F equals -F.
Thus, the equation simplifies to:
-F - 1 = -6 + F.
**Step 3: Isolate Variable Terms**
To isolate the variable F, we want all terms containing F on one side. We can do this by adding F to both sides of the equation:
-F + F - 1 = -6 + F + F,
which simplifies to:
-1 = -6 + 2F.
**Step 4: Move Constant Terms**
Now, let's move the constant -6 to the left side by adding 6 to both sides:
-1 + 6 = 2F,
which gives us:
5 = 2F.
**Step 5: Solve for F**
Finally, to find the value of F, divide both sides by 2:
F = 5 / 2,
which results in:
F = 2.5.
**Conclusion**
The solution to the equation is F = 2.5.
Understanding how to solve linear equations not only aids in completing math homework but also develops critical thinking skills applicable in real-world situations, such as budgeting or calculating distances. Practice with different equations to gain confidence in your skills, and remember, each step is crucial for arriving at the correct answer!
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