Solve 35−2x≤6x−5.
Get the complete, step-by-step math solution for: "Solve (5-2 x)/(3) ≤ (x)/(6)-5.". Powered by SolveForX AI math tutor.
Step-by-Step Solution
Step 1: Clear the denominators
To eliminate the denominators and simplify the inequality, we multiply both sides by the least common multiple (LCM) of the denominators, which are 3 and 6. The LCM of 3 and 6 is 6.
Step 2: Simplify the inequality
After multiplying by 6, we simplify each term. On the left side, 6/3=2, so we have 2(5−2x). On the right side, 6/6=1, so we have x, and 6×5=30.
Step 3: Distribute and combine like terms
Next, we distribute the 2 on the left side: 2×5=10 and 2×(−2x)=−4x. Now, we have a linear inequality with no fractions.
Step 4: Isolate the variable term
To isolate the variable x, we move all terms containing x to one side and constant terms to the other. We add 4x to both sides and add 30 to both sides.
Step 5: Simplify and solve for x
Combine the terms on both sides: 10+30=40 and x+4x=5x. Finally, divide both sides by 5 to solve for x. Since we are dividing by a positive number, the inequality sign remains the same.