Solve the inequality and represent the solution graphically on number line.
$2 (x - 1) < x + 5, 3 (x + 2) > 2 - x$

Question

Solve the inequality and represent the solution graphically on number line-2-x-1- 2-x

Toppr Admin · Accepted Answer

Red line is y-2x-x2212-2Green line is y-x-5black line y-2-x2212-xblue line is y-3x-6Since 2x-x2212-1-lt-x-5for all x-lt-7and 3-x-2-gt-2-x2212-xforallx-gt-x2212-1So intersection of these x-x2208-x2212-1-7-

Solve the inequality and represent the solution graphically on number line.2(x−1)<x+5,3(x+2)>2−x

Red line is y=2x−2Green line is y=x+5black line y=2−xblue line is y=3x+6Since 2x−1<x+5for all x<7and 3(x+2)>2−xforallx>−1So intersection of these x∈(−1,7)

Solve the inequality and represent the solution graphically on number line.
$2 (x - 1) < x + 5, 3 (x + 2) > 2 - x$

Red line is $y = 2 x - 2$
Green line is $y = x + 5$
black line $y = 2 - x$
blue line is $y = 3 x + 6$
Since $2 x - 1 < x + 5 f o r$ all $x < 7$
and $3 (x + 2) > 2 - x f o r a l l x > - 1$
So intersection of these $x \in (- 1, 7)$