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Using the properties of equality, find the solution to the equation 2f/5−8/5+2f=8.

User Icon for Bot GPT 3.5 Bot GPT 3.5 answered
1 year ago

To find the solution to the equation 2f/5 - 8/5 + 2f = 8, we can simplify the equation step by step using the properties of equality.

Step 1: Start by simplifying the fractions on the left side of the equation. The common denominator for the fractions is 5, so we can rewrite the equation as:

(2f + (-8) + 2f) / 5 = 8

Simplifying further gives us:

(4f - 8) / 5 = 8

Step 2: Multiply both sides of the equation by 5 to eliminate the denominator:

5 * (4f - 8) / 5 = 8 * 5

This simplifies to:

4f - 8 = 40

Step 3: Add 8 to both sides of the equation to isolate the variable:

4f - 8 + 8 = 40 + 8

This simplifies to:

4f = 48

Step 4: Divide both sides of the equation by 4 to solve for f:

4f / 4 = 48 / 4

This gives us:

f = 12

So, the solution to the equation 2f/5 - 8/5 + 2f = 8 is f = 12.

User Icon for Step-by-Step Bot Step-by-Step Bot answered
1 year ago

To find the solution to the equation 2f/5 - 8/5 + 2f = 8, we can follow these steps:

Step 1: Combine like terms on the left side of the equation.
2f/5 + 2f - 8/5 = 8

Step 2: To simplify the equation, let's find a common denominator for the fractions and combine them.
(2f + 2f * 5 - 8) / 5 = 8

Step 3: Simplify the numerator.
(2f + 10f - 8) / 5 = 8

Step 4: Combine like terms in the numerator.
(12f - 8) / 5 = 8

Step 5: Multiply both sides of the equation by 5 to eliminate the fraction.
5 * (12f - 8) / 5 = 8 * 5

Step 6: Simplify.
12f - 8 = 40

Step 7: Add 8 to both sides of the equation.
12f - 8 + 8 = 40 + 8

Step 8: Simplify.
12f = 48

Step 9: Divide both sides of the equation by 12 to solve for f.
12f/12 = 48/12

Step 10: Simplify.
f = 4

Therefore, the solution to the equation 2f/5 - 8/5 + 2f = 8 is f = 4.