Hi Jana.
In these equations you will have to apply BEDMAS or BIDMAS . I have answered all the questions but have shown working out for you to learn!
Q1. x = -5
Q2. x = -(15/16).
Q3. x = 14/15.
Q4. x = 31/ 17
Q1.
Step 1. Firstly you need a common denominator, so you will get a common denominator of 6.
Step 2. From [(x-4)/6] - [(2x-2)/6] = 3/6 you will subtract the values and get (x - 4 - 2x + 2) / 6 = 3/6
Step 3. Now you get (-x - 2) / 6 = 3/6.
Step 4. Now, you cross multiply the 6 on the other side of the equation and get - x - 2 = 3.
Step 5. Now, you simply move -2 on the other side of the equation and make it +2
Step 6. From that, -x = 5, and then x = -5.
Therefore x = -5
Q2.
Step 1. Firstly, to make it easier only get a common denominator on the LHS ( Left hand side ) of the equation which will be 60.
Step 2. From the common denominator you will get (40x - 25)/ 60 - (84x + 36)/ 60 = (x-4)15.
Step 3. From subtracting them you get (-44x -61)/ 60 = (x-4)15.
Step 4. Cross multiply the 60 on the RHS, in which you will get 4x - 16.
Step 5. So -44x -61 = 4x - 16
Step 6. By solving the equation you get -48x - 45 = 0
Therefore you get x = -(45/48) which is x = -(15/16).
Q3.
Step 1. Apply the rules before and get common denominator 15.
Step 2. ((27x - 12)/ 15 ) + (5x - 15)/15 = [(2x+1)/15]
Step 3. (32x - 27)/15 = (2x+1)/15
Step 4. Cross multiply and get 32x - 27 = 2x + 1
Step 5. Solve the equation and get 30x = 28
Step 6. x = 28/30
Therefore you get x = 14/15.
Q4.
Step 1. (4x + 20)/ 16 - (3x+7)/16 = (5x-3)/12
Step 2. (x + 13)/ 16 = (5x-3)/12
Step 3. Cross multiply 16: x + 13 = (20x - 12)/3
Step 4.Cross multiply the denominator of 3 in the RHS in the LHS. This makes 3x + 19 = 20x - 12.
Step 5. -17x = -31.
Step 6. From this you get x = 31/17
Therefore your answer is x = 31/ 17
Cheers !
Good luck in your mathematical journey
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