Solution: Let us consider the length of the shortest piece be x cm From the question, length of the second piece = \[(x+3)\]cm Given, length of third piece is to be twice as long as the shortest =...

Solution: Let us consider  the length of the shortest side of the triangle be x cm From the question, length of the longest side = \[3x\] cm Given, third side is  \[2\] cm shorter than the longest...

Solution: Let us consider x be the smaller of the two consecutive even positive integers Then, the other integer  = \[x+2\] According to  the question that, both the integers are larger than \[5\]...

Solution: Let us consider x be the smaller of the two consecutive odd positive integers Then the other integer = \[x+2\] It is given that both the integers are smaller than \[10\] i.e.,...

Solution: Let us consider Sunita scored x marks in her fifth examination From the given question  in order to receive A grade in the course she must have to obtain average \[90\] marks or more in...

Solution: Let us consider x be the marks obtained by Ravi in his third unit test Given that, the entire students should have an average of at least \[60\] marks The inequality based on given...

Solution: The given inequality is \[\frac{x}{2}\ge \frac{(5x-2)}{3}-\frac{(7x-3)}{5}\] After solving we get, \[\frac{x}{2}\ge \frac{5(5x-2)-3(7x-3)}{15}\] Now compute the inequality we get,...

Solution: The inequality given is, \[3(1-x)<2(x+4)\] After Solving the given inequality, we get = \[3-3x<2x+8\] Now after rearranging we get, = \[3-8<2x+3x\] = \[-5<5x\] Divide \[5\] on...

Solution: From the question it is given that, \[5x-3\ge 3x-5\] After solving and rearranging the inequality we get, = \[5x-3x\ge +3-5\] After simplifying we get, \[2x\ge -2\] Divide by 2on both...

Solution: From the question it is given that, \[3x-2<2x+1\] By solving the inequality, we get \[3x-2<2x+1\] = \[3x-2x<2+1\] = \[x<3\] The graph of \[3x-2<2x+1\]is represented below...

Solution: To find inequality of \[\frac{(2x-1)}{3}\ge \frac{(3x-2)}{4}-\frac{(2-x)}{5}\] After rearranging we get, \[\frac{(2x-1)}{3}\ge \frac{15x-10-8+4x}{20}\] = \[\frac{(2x-1)}{3}\ge...

Solution: From the question it is given that \[\frac{x}{4}<\frac{(5x-2)}{3}-\frac{(7x-3)}{5}\] = \[\frac{x}{4}<\frac{5(5x-2)-3(7x-3)}{15}\] After simplifying we get,...

Solution: From the question it is given that, \[37-(3x+5)\ge 9x-8(x-3)\] After simplifying we get = \[37-3x-5\ge 9x-8x+24\] = \[32-3x\ge x+24\] After  rearranging we get = \[32-24\ge x+3x\] = \[8\ge...

Solution: From the question it is given that, \[2(2x+3)-10<6(x-2)\] After multiplying we get \[4x+6-10<6x-12\] After simplifying we get \[-4+12<6x-4x\] \[8<2x\] \[4<x\] The solutions...

Solution: From the question it is given that \[\frac{1}{2}\left( \frac{3x}{5}+4 \right)\ge \frac{1}{3}(x-6)\] After cross-multiplying the denominators, we get \[3\left( \frac{3x}{5}+4 \right)\ge...

Solution: From the question it is given that \[\frac{3(x-2)}{5}\le \frac{5(2-x)}{3}\] After cross – multiplying the denominators, we get \[9(x-2)\le 25(2-x)\] \[9x-18\le 50-25x\] Add  \[25x\] both...

Solution: From the question it is given that \[\frac{x}{3}>\frac{x}{2}+1\] After rearranging and taking LCM we get, \[\left( \frac{2x-3x}{6} \right)>1\] \[-x/6>1\] \[-x>6\] \[x<-6\]...

Solution: From the question it is given that, \[x+\frac{x}{2}+\frac{x}{3}<11\] Take x as common we get, \[x\left( 1+\frac{1}{2}+\frac{1}{3} \right)<11\] Take LCM we get \[x\left(...

Solution: From the question it is given that, \[3(2-x)\ge 2(1-x)\] After multiplying we get \[6-3x\ge 2-2x\] Adding \[2x\] to both the sides, \[6-3x+2x\ge 2-2x+2x\] \[6-x\ge 2\] Now, subtracting...

Solution: From the question it is given that, \[3(x-1)\le 2(x-3)\] Multiply above inequality can be written as \[3x-3\le 2x-6\] Add \[3\]to both the sides, we get \[3x-3+3\le 2x-6+3\] \[3x\le 2x-3\]...