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  • Solve the inequality and represent the solution graphically on number line. 5(2x - 7) - 3( 2x + 3) less than or equal to 0, 2x + 19 less than or equal to 6x + 47

Q: Solve the inequality and represent the solution graphically on number line.5(2x-7)-3(2x+3)\leq 0,\quad 2x + 19 \leq 6x +47

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Given : 5(2x-7)-3(2x+3)\leq 0,\quad 2x + 19 \leq 6x +47

5(2x-7)-3(2x+3)\leq 0\, \, \, \, \, and\, \, \, \, \, \, \, \quad 2x + 19 \leq 6x +47

\Rightarrow \, \, 10x-35-6x-9\leq 0\, \, \, \, \, and\, \, \, \, \, \, \, \quad 2x -6x\leq 47-19

\Rightarrow \, \, 4x-44\leq 0\, \, \, \, \, and\, \, \, \, \, \, \, \quad -4x\leq 28

\Rightarrow \, \, 4x\leq 44\, \, \, \, \, and\, \, \, \, \, \, \, \quad 4x\geq - 28

 \Rightarrow \, \, x\leq 11\, \, \, \, \, and\, \, \, \, \, \, \, \quad x\geq - 7

x\in [-7,11]

The solution graphically on the number line is as shown :

 

Posted by

seema garhwal

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