(x-3)/(6)-(7)/(15)≤(3x-1)/(10)
LCM(6,15,10) = 30, so if you multiply all the terms by 30, you get
5(x-3) - 2(7) <= 3(3x-1)
5x-3-14 <= 9x-3
-4x <= 14
x >= 7/2
To solve the given inequality, let's break it down into smaller steps:
Step 1: Simplify both sides of the equation by finding a common denominator for all fractions involved. In this case, the least common denominator (LCD) is 30.
For the left side, multiply the first fraction by 5/5 and the second fraction by 2/2 to obtain a common denominator of 30:
[(x - 3)(5)] / (6)(5) - [(7)(2)] / (15)(2) ≤ [(3x - 1)(3)] / (10)(3)
Simplifying the numerators and denominators gives us:
(5x - 15) / 30 - 14 / 30 ≤ (9x - 3) / 30
Step 2: Combine the fractions on both sides:
(5x - 15 - 14) / 30 ≤ (9x - 3) / 30
Simplifying the numerators gives us:
(5x - 29) / 30 ≤ (9x - 3) / 30
Step 3: Remove the denominators by multiplying through by 30:
30(5x - 29) / 30 ≤ 30(9x - 3) / 30
Simplifying further:
5x - 29 ≤ 9x - 3
Step 4: Rearrange the equation to isolate the variable:
Subtract 5x from both sides:
-29 ≤ 9x - 5x - 3
Simplify the equation:
-29 ≤ 4x - 3
Step 5: Add 3 to both sides:
-29 + 3 ≤ 4x - 3 + 3
Simplify the equation:
-26 ≤ 4x
Step 6: Divide both sides by 4:
-26 / 4 ≤ 4x / 4
Simplify the equation:
-6.5 ≤ x
So, the solution to the inequality is x ≤ -6.5.