Question

Solve the following inequation, and graph the solution on the number line :

2x - 5 ≤ 5x + 4 < 11, x є R.​

Answer 1

Given : 2x - 5 ≤ 5x + 4 < 11, x є R

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➹ 2x - 5 ≤ 5x + 4 and 5x + 4 < 11

➹ 2x - 5 + (-5x + 5) ≤ 5x + 4 + (-5x + 5) and 5x + 4 + (-4) < 11 + (-4)

➹ -3x ≤ 9 and 5x < 7

➹ x ≥ -3 and x < 7/5

➹ -3 ≤ x < 7/5

➹ -3 ≤ x < 7/5 where x є R

∴ The solution set = { x : x є R, -3 ≤ 7/5 }

• The graph of the solution set is shown by the thick portion of the number line. The solid circle at -3 indicates that the number -3 is included among the solutions and the open circle at 7/5 indicates that the number 7/5 is not included among the solutions.

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Answer 2

Answer in attachment

Hope it helps you