Need help with these algebraic equations?

Question

I really don't understand how to do these. Could someone walk me through the steps? Thank you.

x/3 + 3x/4 = 2

(17+x)/x + (32+x)/x = 100

(100-4x)/3 = (5x+6)/4 + 6

Answer 1

x/3 + 3x/4 = 2

[4x + 9x]/12 = 2

13x = 24



x = 24/13

Check 24/(13*3) + 3*24/(13*4) = 8/13 + 18/13 = 26/13 = 2  it is correct

(17+x)/x + (32+x)/x = 100

(17+x)  + (32+x) = 100x

   49 + 2x = 100x

        49 = 98x

          x = 1/2

Check is this correct

(17+1/2)/(1/2) + (32+1/2)/(1/2) = 2(17.5) + 2(32.5) = 35 + 65 = 100

It is correct.

(100-4x)/3 = (5x+6)/4 + 6

(100-4x)*4/12 - (5x+6)*3/12 =  6

400-16x - 15x - 18 = 72

400-90 = 31x

310 = 31x

x = 10

Check is this correct

(100-40)/3 = 60/3 = 20

(50+6)/4 + 6 = 56/4+6 = 14+6 = 20

It is correct

Answer 2

x/3 + 3x/4 = 2 ← Note: Multiply all terms by least common multiple which in this case is 12.

12(x/3) + 12(3x/4) = 12(2)

4x + 9x = 24

13x = 24

13x/13 = 24/13

x = 24/13

(17+x)/x + (32+x)/x = 100 ← Note: Combine like terms and then cross multiply.

(17 + x + 32 + x)/x = 100

(2x + 49)/x = 100

2x + 49 = 100x

2x + 49 - 2x = 100x - 2x

49 = 98x

49/98 = 98x/98

x = 49/98 or 1/2

(100-4x)/3 = (5x+6)/4 + 6 ← Note: Multiply all terms by least common multiple which in this case is 12.

12[(100-4x)/3] = 12[(5x+6)/4] + 12[6]

4(100 - 4x) = 3(5x + 6) + 72

400 - 16x = 15x + 18 + 72

400 - 16x = 15x + 90

400 - 16x - 15x = 15x + 90 - 15x

400 - 31x = 90

400 - 31x - 400 = 90 - 400

-31x = -310

(-31x)/(-31) = -310/(-31)

x = 10