Please help me, these fractions are tripping me up.
11(x/4)-4(x/3)+12=2(x/3)-9(x/4)
I know that first you do this:
11x/4 - 4x/3 +12= 2x/3-9x/4
That's as far as i can go
combine fractions with matching denominators
20x/4 + 12 = 6x/3
reduce fractions ... 5x + 12 = 2x
To solve the equation 11(x/4) - 4(x/3) + 12 = 2(x/3) - 9(x/4), we need to eliminate the fractions. Here's how you can approach this:
Step 1: Multiply every term in the equation by the least common multiple (LCM) of the denominators, which in this case is 12. The purpose of this is to clear the fractions.
12 * [11(x/4) - 4(x/3) + 12] = 12 * [2(x/3) - 9(x/4)]
This simplifies to:
(12 * 11)(x/4) - (12 * 4)(x/3) + (12 * 12) = (12 * 2)(x/3) - (12 * 9)(x/4)
Step 2: Simplify the equation using the distributive property:
33x/4 - 16x/3 + 144 = 8x/3 - 108x/4
Step 3: Combine like terms on both sides of the equation:
33x/4 + 108x/4 - 16x/3 - 8x/3 = -144
(33x + 108x)/4 - (16x + 8x)/3 = -144
141x/4 - 24x/3 = -144
Step 4: Find a common denominator for the remaining fractions. The LCM of 4 and 3 is 12, so we multiply the fractions by 3/3 and 4/4 respectively to obtain:
(141x * 3)/(4 * 3) - (24x * 4)/(3 * 4) = -144
423x/12 - 96x/12 = -144
Step 5: Combine like terms:
(423x - 96x)/12 = -144
327x/12 = -144
Step 6: Isolate x by multiplying both sides of the equation by the reciprocal of the coefficient of x on the left side:
[(12 * 327x)/12] * (1/327) = -144 * (1/327)
x = -144/327
x ≈ -0.4402
So, the solution to the equation is x ≈ -0.4402.