Question

Solution of 2y-3< y+1 < 4y+4 is: * -2 < y < 4 2 ​

Answer 1

Given inequation, 2y–3<y+1≤4y+7

So, we have

2y−3<y+1 and y+1≤4y+7

⇒2y−y<1+3 and y−4y≤7–1

⇒y<4 and −3y≤6

⇒y<4 and −y≤2⇒y≥−2

⇒−2≤y<4

The solution set is {y:−2≤y<4,y∈R}

Representing the solution on a number line:

Answer 2

$\Large\mathtt\green{ }\huge\underline\mathtt\red{Answer : }$

2y – 3 < y + 1 ≤ 4y + 7, y ∈ R

⇒ 2y – 3 – y < y + 1 – y ≤ 4y + 7 – y

⇒ y – 3 < 1 ≤ 3y + 7

⇒ y – 3 < 1 and 1 ≤ 3y + 7

⇒ y < 4 and 3y ≥ 6 ⇒ y ≥ – 2

⇒ – 2 ≤ y < 4

The graph of the given equation can be represented on a number line as: