Find the mistake in the following set of steps in a student’s attempt to solve 5xx+2≥xx+25, for xx. what is the correct solution set?
5x+2≥x+2/5
5(x+2/5)≥x+2/5 (factoring out 5 on the left side)
5≥1 (dividing by (x+2/5))
so, the solution set is the set of all real numbers.

x ≥ -3/5

Step-by-step explanation:

The mistake:  

dividing by (x+2/5)

At the left side of the inequality we have a factor ( x + 2/5 ) and you can divide, but to keep the inequality you have to do the same at the right hand side of the inequality and x+ 2/5 are two terms. You can pass x + 2/5 to the right  shanging their sign as follow

5*(x+2/5) -x -2/5 ≥ 0     ⇒ 5x + 2 - x -2/5 ≥ 0  

4x + 2 + 2/5 ≥0    ⇒     4x + 12/5 ≥ 0     ⇒    ( 20x + 12)/5 ≥ 0

20x + 12 ≥0       ⇒20x ≥-12     x ≥ - (12/20)   or x ≥ -3/5

find the magnitude of the trig term  

csc

(

x

)

−

1

by taking the absolute value of the coefficient.

1

find the lower bound of the range.

tap for more

y

=

−

2

find the upper bound of the range.

tap for more

y

=

0

the range is  

y

≤

−

2

or  

y

≥

0

.

(

−

∞

,

−

2

]

∪

[

0

,

∞

)

{

y

|

y

≤

−

2

,

y

≥

0

}

step-by-step explanation: