x/2 - (3x+1/3) < 1/4
My answer was x > -0.25 , but im not positive.
Multiply by 12.
6x - 36x - 4 < 3
Combine terms.
-30x < 7
x > -7/30 = -0.233333
No sorry i mean x/2 - (3x+1)/3 < 1/4
To solve the inequality x/2 - (3x + 1/3) < 1/4, follow these steps:
Step 1: Distribute the negative sign to (3x + 1/3) and simplify:
x/2 - 3x - 1/3 < 1/4
Step 2: Find a common denominator for the fractions. The least common denominator (LCD) between 2 and 3 is 6. Multiply each term by 6 to clear the fractions:
6(x/2) - 6(3x) - 6(1/3) < 6(1/4)
3x - 18x - 2 < 3
Step 3: Combine like terms on the left side:
-15x - 2 < 3
Step 4: Isolate the variable x by moving the constant term to the right side:
-15x < 3 + 2
-15x < 5
Step 5: Divide both sides of the inequality by the coefficient of x, which in this case is -15. Note that when dividing by a negative number, the inequality sign flips direction:
x > 5/-15
x > -1/3
Step 6: Simplify the fraction:
x > -1/3
Therefore, the correct solution to the inequality x/2 - (3x + 1/3) < 1/4 is x > -1/3.
It seems there was a mistake in your initial answer. The correct solution is x > -1/3, not x > -0.25.