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We'll remove the brackets from both sides:
3x - 6 > 8x + 44
We'll move all terms in x to the left and all numbers to the right:
3x - 8x > 6 + 44
- 5x > 50
We'll divide by -5 and we'll change the direction of inequality:
x < -50/5
x < -10
The values that make the inequality to hold belong to the opened interval (-`oo` ; -10).
We mutiply out of the brackets so that it could be omitted
3x-6 > 8x+44
Remember, if you multiply or divide an inequality by a negative number, CHANGE the sign of the equation. (Even college students make those mistakes).
This is the solution to the inequality
Writing as an interval form like what giorigana1976 did was no wrong, but x<-10 is simpler and easier to understand. Moreover, writing as an internal omits the variable, leaving the teacher confused about what variable you are solving. Most of all, do what your teacher says and you would be ok.
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