%E2%89%A51%2F3(x-6).jpeg "1/2(3x/5+4)≥1/3(x-6)")
Solving the Inequality 1/2(3x/5+4)≥1/3(x-6)
In this article, we will solve the inequality 1/2(3x/5+4)≥1/3(x-6) step by step.
Step 1: Simplify the Left-Hand Side (LHS)
Let's start by simplifying the left-hand side of the inequality:
1/2(3x/5+4) = 1/2(3x/5) + 1/2(4) = 3x/10 + 2
Step 2: Simplify the Right-Hand Side (RHS)
Now, let's simplify the right-hand side of the inequality:
1/3(x-6) = x/3 - 2
Step 3: Write the Inequality
Now that we have simplified both sides, we can write the inequality as:
3x/10 + 2 ≥ x/3 - 2
Step 4: Solve the Inequality
Let's solve the inequality by multiplying both sides by 30 to eliminate the fractions:
9x + 60 ≥ 10x - 60
Subtract 60 from both sides:
9x ≥ 10x - 120
Subtract 10x from both sides:
-x ≥ -120
Divide both sides by -1 (and flip the inequality sign):
x ≤ 120
Conclusion
Therefore, the solution to the inequality 1/2(3x/5+4)≥1/3(x-6) is x ≤ 120.
