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The solution set of 6≤−3(2x−4)<126 \leq -3(2x - 4) < 12, x∈Rx \in R is:

Solution

✅ Correct Option: 1

Start with 6≤−3(2x−4)<126 \leq -3(2x - 4) < 12

Distribute −3-3 into the brackets:

6≤−6x+12<126 \leq -6x + 12 < 12


The compound inequality means both conditions must be true:

Left part: 6≤−6x+126 \leq -6x + 12

Right part: −6x+12<12-6x + 12 < 12


For the left part:

6≤−6x+126 \leq -6x + 12

6−12≤−6x6 - 12 \leq -6x

−6≤−6x-6 \leq -6x

Dividing both sides by −6-6 (the inequality sign flips when dividing by a negative number):

1≥x1 \geq x

x≤1x \leq 1


For the right part:

−6x+12<12-6x + 12 < 12

−6x<0-6x < 0

Dividing both sides by −6-6 (the inequality sign flips):

x>0x > 0


Both conditions must be true together:

x≤1x \leq 1 and x>0x > 0

Therefore: 0<x≤10 < x \leq 1


In interval notation:

(0,1](0, 1]

where (( means 0 is not included and ]] means 1 is included.

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