Solve for x (3x-1)/4-(x-5)/5>-2

Problem

(3*x−1)/4−(x−5)/5>−2

Solution

1. Find a common denominator for the fractions on the left side, which is 20

2. Multiply every term in the inequality by 20 to eliminate the denominators.

20⋅(3*x−1)/4−20⋅(x−5)/5>20⋅(−2)

3. Simplify the terms by performing the division.

5*(3*x−1)−4*(x−5)>−40

4. Distribute the constants into the parentheses.

15*x−5−4*x+20>−40

5. Combine like terms on the left side of the inequality.

11*x+15>−40

6. Isolate the variable term by subtracting 15 from both sides.

11*x>−55

7. Solve for x by dividing both sides by 11

x>−5

Final Answer

(3*x−1)/4−(x−5)/5>−2⇒x>−5

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