When solving the inequality \(7f + 18 \leq 4f + 10\), the goal is to isolate the variable \(f\) on one side. To do this effectively, we want to eliminate \(f\) terms from one side of the inequality.
Here's a step-by-step breakdown of why you would subtract \(4f\) first:
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Identify terms with \(f\): You have \(7f\) on the left side and \(4f\) on the right side. The goal is to combine these terms so that all \(f\) terms are on one side.
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Choose the appropriate operation: Since \(7f\) is greater than \(4f\), subtracting \(4f\) from both sides will simplify the inequality. This will help you to move all \(f\) terms to the left side, making the equation easier to work with.
So, subtract \(4f\) from both sides:
\[ 7f + 18 - 4f \leq 4f + 10 - 4f \]
This simplifies to:
\[ 3f + 18 \leq 10 \]
- Continuing to isolate: You would continue to isolate \(f\) by subtracting \(18\) from both sides:
\[ 3f \leq 10 - 18 \] \[ 3f \leq -8 \]
- Final step: Finally, divide both sides by \(3\):
\[ f \leq -\frac{8}{3} \]
In summary, subtracting \(4f\) first is a strategic step that allows you to simplify the inequality by consolidating all variable terms onto one side. This approach is a standard method in solving both equations and inequalities as it helps maintain clarity and organization throughout the solution process.
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