Question

would this have no solution or all reals ?
5|x+2|>10

Answer 1

5|x+2|>10

|x+2|>10/5

|x+2|>2

x+2>2 or x+2 < -2

From here, solve each inequality.

Answer 2

got it thanks

Answer 3

you're welcome

Answer 4

@jim_thompson5910 i have another question like it, but itnstead its -10 ... would i just flip the signs?

Answer 5

you mean it's

5|x+2|>-10

???

Answer 6

yes

Answer 7

Follow the same steps, but at the end, it's slightly different.

5|x+2|>-10

|x+2|>-10/5

|x+2| > -2

But since the absolute value of any number is always either 0 or positive, this means that |x+2| is ALWAYS greater than ANY negative number.

So |x+2| > -2 has an infinite number of solutions since you can plug in any real number for x and it will be true.

Answer 8

no solution?

Answer 9

infinitely many solutions

Answer 10

so all real numbers?

Answer 11

yes

Answer 12

This is because you can plug in any real number and it will work.

Answer 13

alrighty , thanks again