Solve. |\frac{6x+2}{4}|>4

Linda Seales

Linda Seales

Answered question

2021-12-14

Solve.
|6x+24|>4

Answer & Explanation

Timothy Wolff

Timothy Wolff

Beginner2021-12-15Added 26 answers

Step 1
Apply the properties of absolute value function, to remove the modulus sign in the given inequality.
If |x|>a, a>0 then x>a or -x>a.
|6x+24|>4
(6x+24)>4...(1)
(6x+24)>4
(6x+24)<4...(2)
Step 2
To find the value of x, multiply by 4, then subtract 2 and divide by 6 on both sides of the inequalities (1) and (2).
6x+24>4
(6x+24)(4)>(4)(4)
6x+2>16
6x>16-2
>14
6x6>146
x>73
6x+24<4
(6x+24)(4)<(4)(4)
6x+2<-16
6x<-16-2
<-18
6x6<186
x<-3
Hence, x<-3 or x>73.

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