Algebra: solving (6X + 5) / 3 = [3X / 7] - 2

[ricacruz]

I am really having trouble figuring this one problem out. My math is not that great, but I am trying. I understand the order of operations, using the reciprocal to eliminate a fraction. Nevertheless, I am really stuck on this problem and do not know how to begin it. Can someone help or check my answer if it is correct?

(6X+5)/3 = [3X/7]-2
3*(6X+5) = [3X/7] -6 (Multiply both sides by 3)
18X+15 = 3X/7 -6 (Removed brackets)
3X*18X+15 = (3X) 3X/7 -6 (Multiply both sides by 3)
54X+15 = 7 - 6
54X = 7-6-15
54X = -14
X = -14/54

 

[Mrspi]

Re: Algebra

I am really having trouble figuring this one problem out. My math is not that great, but I am trying. I understand the order of operations, using the reciprocal to eliminate a fraction. Nevertheless, I am really stuck on this problem and do not know how to begin it. Can someone help or check my answer if it is correct?

(6X+5)/3 = [3X/7]-2
3*(6X+5) = [3X/7] -6 (Multiply both sides by 3)
18X+15 = 3X/7 -6 (Removed brackets)
3X*18X+15 = (3X) 3X/7 -6 (Multiply both sides by 3)
54X+15 = 7 - 6
54X = 7-6-15
54X = -14
X = -14/54

You have TWO fractions. The denominator of one of them is 3. The denominator of the other one is 7. The least common multiple of 3 and 7 is 21. Multiply both sides of the equation by 21:

21 * [(6x + 5) / 3 ] = 21*(3x / 7) - 21*2

Each denominator divides into the multiplier of 21. So, you should now have this:

7(6x + 5) = 3(3x) - 42

Now...you should be able to continue with this to find the value of x. Be sure to check your solution by substituting into the original equation. If the original equation is true when you substitute the value you got for x, you know you've solved correctly.

 

[Loren]

Re: Algebra

6X+5)/3 = [3X/7]-2
3*(6X+5) = [3X/7] -6 (Multiply both sides by 3) <<< Wrong
\(\displaystyle 3\cdot\frac{6x+5}{3}=3(\frac{3x}{7} - 2)\) becomes \(\displaystyle 6x+5 = \frac{9x}{7}-6\). Now, proceed from there.

18X+15 = 3X/7 -6 (Removed brackets)
3X*18X+15 = (3X) 3X/7 -6 (Multiply both sides by 3)
54X+15 = 7 - 6
54X = 7-6-15
54X = -14
X = -14/54