Question

Match the compound inequalities

Answer 1

I one is 8x<24 and -8≤2x-4

Hence x <24/8 =3 and -4≤2x:  divide by positive 2 to get -2≤x

Hence solution is -2≤x<3

Therefore c is the correct matching for 1.

2) 5x-2>13 or -4x≥8  

i.e. 5x>15 or x≤8/(-4) = -2 (since dividing by negative inequality reverses)

Or x>3 or x ≤-2

Hence solution is two regions to the right of 3 excluding 3 and left of -2 including -2.

Graph b is the correct match.

3) -25≤9x+2<20

Subtract 2

-27≤9x<18: Now divide by positive 9

-3≤x<2

Hence graph is the region between -3 and 2 including only -3.

Graph a is correct matching for question 3.