Solve the inequality. Write the solution in interval notation.

Question

 4(x+1)+2>=3x+6

Answer 1

Distribute the 4, 4x +4 +2 >= 3x +6

Combine like terms on left side, no need to on right side since it is already combined

 

4x + 6 >= 3x +6

 

subtract 3x from both sides, 4x + 6 -3x >= 3x +6 - 3x, becomes 4x + 6 -3x >= 3x +6 - 3x,   x + 6 >= 6

 

Subtract 6 from each side x + 6 - 6 >= 6 - 6,       x + 6 - 6 >= 6 - 6, becomes    x >= 0

 

Interval notation: [0, infinity)   

 

**we use a [ because of the >=  If it was just > we would use (, since you really can't have infinity we use a ) but a ] should be incorrect either.