Solve the following systems of linear in equations: 3x – x > x + 4 /3 >3

Question

Solve the following systems of linear in equations:

3x – x > x + ^{\(\cfrac{4-{\text{x}}}{3}\)} > 3

Answer 1

Subtracting x from both the sides in above equation

2x – x > x +  \(\cfrac{4-{\text{x}}}{3}\) - x

x > \(\cfrac{4-{\text{x}}}{3}\)

Multiplying both the sides by 3 in the above equation

3x > 3 \(\bigg(\cfrac{4-{\text{x}}}{3}\bigg)\)

3x > 4 – x

Adding x on both the sides in above equation 

3x + x > 4 -x + x 

4x > 4

Dividing both the sides by 4 in above equation

\(\frac{4{\text{x}}}{4} > \frac{4}{4}\)

x > 1 

Now when,

x + \(\cfrac{4-{\text{x}}}{3}\) > 3

Multiplying both the sides by 3 in above equation

3x + 3\(\bigg(\cfrac{4-{\text{x}}}{3}\bigg)\) > 3(3) 

3x + 4 – x > 9 

2x + 4 > 9

Subtracting 4 from both the sides in above equation 

2x + 4 – 4 > 9 – 4 

2x > 5 

Dividing both the sides by 2 in above equation

Merging overlapping intervals