SOLUTION: can you please help me solve this problem step by step. This is linear inequalities probelm 5(x+1)<3x+4 = Thanks

Question 127367: can you please help me solve this problem step by step. This is linear inequalities probelm 5(x+1)<3x+4 =
Thanks
Found 2 solutions by edjones, solver91311:
Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
5(x+1)<3x+4
5x+5<3x+4
5x-3x+5-5<3x-3x+4-5 Add -3x and -5 to each side to get all the x's on one side and numerals on the other.
2x<-1
2x/2<-1/2
x<-.5
.
Ed

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Solve inequalities the same way you solve equations, with two important exceptions. First, if you multiply or divide both sides of the inequality by a negative number, you must reverse the sense of the inequality.

For example, we know it is true that , but if we multiply both sides of the inequality by -1, we get 2 on the left and -1 on the right. The 'less than' symbol is no longer correct, it must be changed to 'greater than' because

The second exception is that the solution set will be represented by an interval rather than a single value.

Distribute and remove parentheses

Add -3x to both sides

Add -5 to both sides

Finally, divide both sides by 2
and the solution set is {x| x is real, }. You can also use interval notation (,). Note the parentheses around the interval. Had the problem included the possiblity of equality, i.e. had it been , then the interval would have been denoted by
(,].
Since we never multiplied or divided by a number that is <0, the sense of the inequality remains as it was in the original inequality.
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