To solve the inequality, we first need to find a common denominator for the two fractions on the left-hand side of the inequality.
The common denominator for 3 and 2 is 6.
Multiplying the first fraction by 2/2 and the second fraction by 3/3, we get:
2(x-2)/6 - 3(x+1)/6 < 6/1
Simplifying each fraction, we get:
(x-2)/3 - (x+1)/2 < 6
To get rid of the fractions, we can multiply both sides of the inequality by 6, the common denominator:
2(x-2) - 3(x+1) < 36
Expanding the brackets, we get:
2x - 4 - 3x - 3 < 36
Simplifying, we get:
-x - 7 < 36
Adding 7 to both sides, we get:
-x < 43
Multiplying both sides by -1 and reversing the inequality, we get:
x > -43
Therefore, the solution set to the inequality is:
x > -43.
Solve the inequality
x-2 x +1<6
------ - --------
3 2
1 answer
1 answer