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

(i)
`x\leq 5`

(ii)
`x\geq 5`

(iii)
`x>5`

(iv)
`x<5`

Explanation:

(i) Two less than
`(3)/(2)` of a number (x) is no more than
`5(1)/(2)`,

⇒ Two less than
`(3)/(2)` of x is less than equal to
`5(1)/(2)`,

`\implies (3)/(2)x-2\leq 5(1)/(2)`

`(3x-4)/(2)\leq (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`