Question

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 1

Answer:

(i)   $x\leq 5$

(ii)   $x\geq 5$

(iii)  $x>5$

(iv)  $x<5$

Step-by-step explanation:

(i) Two less than $\frac{3}{2}$ of a number (x) is no more than $5\frac{1}{2}$,

⇒ Two less than $\frac{3}{2}$ of x is less than equal to $5\frac{1}{2}$,

$\implies \frac{3}{2}x-2\leq 5\frac{1}{2}$

$\frac{3x-4}{2}\leq \frac{11}{2}$

$3x-4\leq 11$

$3x\leq 15$

$\implies x\leq 5$

(ii) The sum of two times a number (x) and -2 is at least 8,

$\implies 2x+(-2) \geq 8$

$2x-2\geq 8$

$2x\geq 10$

$x\geq 5$

(iii) Seven subtracted from 4 times a number (x) is more than 13,

$\implies 4x-7>13$

$4x>20$

$\implies x>5$

(iv) Four added to 3 times a number (x) is less than 19.

$3x+4<19$

$3x<15$

$\implies x<5$