x/5 -x/4 < x-5/5
Show me how to slove the problem.
I will assume you meant x/5 -x/4 < (x-5)/5
multiply each term by 20 to get
4x - 5x < 4x - 20
-5x < -20
x > 4
To solve the inequality x/5 - x/4 < (x-5)/5, follow these steps:
Step 1: Get rid of the fractions by finding a common denominator. In this case, the common denominator is 20. Multiply each term by 20 to obtain:
20 * (x/5) - 20 * (x/4) < 20 * ((x-5)/5)
4x - 5x < 4(x - 5)
Step 2: Simplify the expressions on both sides and distribute the 4 into (x - 5):
4x - 5x < 4x - 20
Step 3: Combine like terms:
-x < 4x - 20
Step 4: Isolate the variable. To do this, move all x terms to the left side:
-x - 4x < -20
-5x < -20
Step 5: Divide both sides of the inequality by -5. Remember that when dividing or multiplying an inequality by a negative number, the direction of the inequality sign changes:
(-5x)/-5 > (-20)/-5
x > 4
So, the solution to the inequality is x > 4.