Question

solve the inequalities and represent the solution graphically on number line : 3x - 7 < 5 + x , 11 - 5x _< 1

Answer 1

1 ) 3x - 7 < 5 + x

3x - x < 5 + 7

2x < 12

x < 12/2

x < 6

draw x = 6 line on a graph .

and shade the region x < 6 which is shown in

the graph red color.

2 ) 11 - 5x ≤ 1

- 5x ≤ 1 - 11

- 5x ≤ - 10

divide bothsides with - 5 , we get

( - 5x )/( - 5 ) ≥ ( - 10 )/( - 5 )

x ≥ 2

draw a line x = 2 , and shaded region which

shown in black lines .

I hope this helps you.

: )

Answer 2

Given that,

3x – 7 > 5x – 1

Now by adding 7 to both the sides, we get

3x – 7 +7 > 5x – 1 + 7

3x > 5x + 6

Again by subtracting 5x from both the sides,

3x – 5x > 5x + 6 – 5x

-2x > 6

Dividing both sides by -2 to simplify we get

-2x/-2 < 6/-2

x < -3

∴ The solutions of the given inequality are defined by all the real numbers less than -3.

Hence the required solution set is (-∞, -3)