Solve the inequalities for x, and match each solution to its number line graph.Two less than 3/2 of a number (x) is no more than 5 1/2 . The sum of two times a number (x) and -2 is at least 8. Seven subtracted from 4 times a number (x) is more than 13. Four added to 3 times a number (x) is less than 19. Pairs Number Line Graph Inequality

Answer:(i)   [tex]x\leq 5[/tex](ii)   [tex]x\geq 5[/tex](iii)  [tex]x>5[/tex](iv)  [tex]x<5[/tex]Step-by-step explanation:(i) Two less than [tex]\frac{3}{2}[/tex] of a number (x) is no more than [tex]5\frac{1}{2}[/tex],⇒ Two less than [tex]\frac{3}{2}[/tex] of x is less than equal to [tex]5\frac{1}{2}[/tex],[tex]\implies \frac{3}{2}x-2\leq 5\frac{1}{2}[/tex][tex]\frac{3x-4}{2}\leq \frac{11}{2}[/tex][tex]3x-4\leq 11[/tex][tex]3x\leq 15[/tex][tex]\implies x\leq 5[/tex](ii) The sum of two times a number (x) and -2 is at least 8,[tex]\implies 2x+(-2) \geq 8[/tex][tex]2x-2\geq 8[/tex][tex]2x\geq 10[/tex][tex]x\geq 5[/tex](iii) Seven subtracted from 4 times a number (x) is more than 13,[tex]\implies 4x-7>13[/tex][tex]4x>20[/tex][tex]\implies x>5[/tex](iv) Four added to 3 times a number (x) is less than 19. [tex]3x+4<19[/tex][tex]3x<15[/tex][tex]\implies x<5[/tex]