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

Respuesta :

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]

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