Question

Please help me solve this. 5 |1/2r + 3| > 5 I

Answer 1

5 |1/2r + 3| > 5 

Divide each side with 5 .

 |1/2r + 3| > 1

For absolute equations, we have two equations 

1/2r + 3 > 1

and -(1/2r + 3) > 1 .

Now solve for 1/2r + 3 > 1

Subtract 3 from each side .

1/2r +3 -3 > 1 - 3

1/2r > -2

Multiply each side by 2 .

(1/2r)*2 > -2*2

r > -4

Now consider  -(1/2r + 3) > 1 

 Multiply each side by negative one and to flip the symbol.

1/2r + 3 < -1 

1/2r  < -1 -3

1/2r  < -4

r < -4*2

r < -8

So the solutions for the equation are r < -8 and  ​r > -4 .