Question

Solve : 4(x + 2)-3(2-x) = 3(x+4)-214--x)​

Answer 1

Step-by-step explanation:

Given, P={x : 5<2x−1≤11,x∈R}  and  Q={x : −1≤3+4x<23,x∈I}

Solving for P,

5<2x−1≤11

⇒5+1<2x≤11+1

⇒6<2x≤12

⇒3<x≤6

Hence, P={x : 3<x≤6,x∈R}

The solution P is represented on number line (a).

Next, solving for Q

−⇒1≤3+4x<23

⇒−1−3≤4x<23−3

⇒−4≤4x<20

⇒−1≤x<5

As Q∈I

Hence, solution Q={−1,0,1,2,3,4}

The solution Q is represented on number line (b).

Therefore, P∩Q={4}

Answer 2

$4(x - 2) - 3(2 - x) = 3(x + 4) - 214 - x$

$4x - 8 - 6 + 3x = 3x + 12 - 214 - x$

$7x - 14 = 2x - 202$

$7x - 2x = - 202 + 14$

$5x = - 188$

$x = \frac{ - 188}{5}$

$x = 37.6$