How do I solve an inequality?
How do I solve these inequalities? 1. x² + 2x - 15 ≤ 0 2. 2p² - 7p + 3 > 0 3. z(2 - z) < z - 12 I don't care whether you are first to answer, or last. Please just explain it clearly step by step. I have been doing other inequalities, so I'm not a complete n00b, these are just slightly harder than the rest, and for example in the first one I can't see how to get rid of the x squared without making the first side more confusing! Thanks!
Solve the inequality: 5x-7<2x-1?
x<2 is the correct answer Subtract 2x from both sides 5x-7<2x-1 becomes 3x-7<-1 Add 7 to both sides 3x-7<-1 becomes 3x<6 Then isolate the x by dividing by 3 3x<6 becomes x<2 You can check this answer by substituting #'s. Any number you substitute greater than 2 will make you inequality wrong and any number bigger less than two will be correct.
How do you solve this inequality, 4 + 2x > 3, and this inequality, 2 + 3 (x - 4) < 3 (2x - 5)?
Let's solve each inequality one by one.• 4+2x>3Subtracting 4 from both sides2x>-1Dividing by 2 on both sidesx>-1/2• 2+3(x-4)<3Simplifying,3(x-4)<1=> x-4<1/3=> x<13/3So, -1/2
How do I solve the inequality [math]x (x-1) (x+2) > 0[/math]?
The question is x(x-1)(x+2)>0Firt ignore the '>' sign:so: x(x-1)(x+2)=0Since 3 numbers are multiplied to give 0, then each may potentially be zero, so: x = 0 x - 1 = 0, which means x = 1 x + 2 = 0, which means x = -2So, you have 3 numbers -2, 0, 1 Now, draw a straight line and mark these 3 points on the line. You can see now that it these numbers have divided the line into 4 different regions. Region 1 is (-inf, -2) -- that is all numbers to the left of -2.Region 2 is (-2,0) --- that is all numbers between -2 and 0Region 3 is (0,1) --- that is all numbers between 0,1Region 4 is (1,inf)--- that is all numbers to the right of 1 Your strategy now, is to test a number inside of each of these 4 regions. Basically you pick a number inside, but not the end values. You substitute the number into the original inequality for x, and see which ones are true.Hence:Region 1: (-inf, -2), I can choose -5 since its in the region to the left of -2.I get: (-5)(-5-1)(-5+2) >? 0 I used '?' because I am not sure if it is trueso: (-5)(-6)(-3) >? 0 Finally -90 >? 0 is false. SO Mark this region with an X on your lineRegion 2: (-2,0), I can choose -1 since its between -2 and 0.I get: (-1)(-1-1)(-1+2) >? 0 I used '?' because I am not sure if it is trueso: (-1)(-2)(1) >? 0 Finally 2 >? 0 is True. SO Mark this region with an check mark on your lineRegion 3: (0,1), I can choose 0.5 since its between 0 and 1.I get: (0.5)(0.5-1)(0.5+2) >? 0 I used '?' because I am not sure if it is trueso: (0.5)(-0.5)(2.5) >? 0 Finally -0.625>? 0 is false. SO Mark this region with an X on your lineFinally: Region 4: (1,inf), I can choose 5 since its in the region to the right of 1.I get: (5)(5-1)(5+2) >? 0 I used '?' because I am not sure if it is trueso: (5)(4)(7) >? 0 Finally 140 >? 0 is true. SO Mark this region with a check on your lineFinally: We have 2 regions that were true (check marks)Regions 2 and 4: (-2,0) and (1,inf)We write them together using the U (for union)Final answer: (-2,0) U (1,inf)
How do we solve gender inequality?
Here are some ways for tackling gender inequality:Political participation of women: Most importantly, include more women in decision-making. Policies, schemes and government facilities are for the entire population. It seems illogical to exclude the voices of half of the population while making vital decisions for the country. The opinions and problems of grassroots women need to be addressed. Like, even if more schools are opened in rural areas, girls don’t always avail those facilities, because mostly they are entrusted with household chores or avoid travelling long distances out of fear of being sexually assaulted.Encourage girls and their parents: One of the key barriers is a mindset that limits what girls can achieve. It would be very helpful if young girls have role models to look up to. The number of women in technology is few and far between. As more women start entering this field, they shall act as examples for younger girls to follow. We need to take measures to build the confidence of girls in tech related subjects.Empower mothers: Empowering mother is important because then they would be free to make their own choices and help their daughters do the same.Change work culture: Gender unequal practices in workplaces are still rampant. It’s high time that every industry, company and enterprise pay equally for equal work.Stop violence: Gender inequality and violence against women and interrelated. According to UN reports, one in three women is likely to experience violence in her lifetime. The world needs to stand up against this and spread awareness about endemic gender based violence that hinders the growth and well-being of women and girls. Apart from the government, NGOs and activists have a crucial role to play in educating the public. Missing Link Trust, a NGO based in Kolkata, is one such organization that is using art and technology to spread awareness about the various problems that women face, trafficking for sexual exploitation being the most important of those.
How do I solve the inequality [math]x^2-2x>0[/math]?
Here’s a unorthodox approach. Suppose that [math]f(x)=x^2–2x[/math]Let us solve the equation [math]f(x)=0[/math][math]x^2–2x=0\tag*{}[/math]Factor the left side[math]x(x-2)=0\tag*{}[/math]Now apply the zero product rule to obtain[math]x=0,2\tag*{}[/math]Time to create a wave :)Look at the solutions, which one is bigger? [math]x=2[/math], so plug in something bigger than [math]x=2[/math] into the function, it gives you positive value.every root occurs once, so function changes sign every time it crosses a root.Now look at the wave, which parts give you positive?We have positive function value when we go onto the right side from [math]x=2[/math], and onto the left side from [math]x=0[/math]Therefore, the solution to [math]x^2–2x>0[/math] is [math]\boxed{(-\infty,0)\cup(2,\infty)}[/math]Read more about Wavy curve method
How do I solve sin2x = 2cos^2x?
Substitute sin2x = 2sinxcosx And you'll get 2sinxcosx = 2cos²x sinxcosx = cos²x sinxcosx - cos²x = 0 cosx(sinx - cosx) = 0 Thus either cosx = 0 or sinx - cosx = 0. From cosx = 0 you get solutions x = &pi/2 and x = 3&pi/2 and from sinx - cosx = 0 sinx = cosx (divide by cosx) tanx = 1 x = &pi/4 and x = 5&pi/4 => So all the solutions in the interval [0, 2&pi] are x = &pi/4, &pi/2, 5&pi/4 and 3&pi/2 (or, equivalently, 45, 90, 225 and 270 degrees) Hope this helps.
Solve the inequality |x + 3a| > 2|x − 2a| where a is a positive constant?
Square both sides and move all terms to LHS : (x+3a)²−(2x−4a)² > 0 Factorize : (x+3a−2x+4a)(x+3a+2x-4a) > 0 → (7a−x)(3x−a) > 0 An easier form to deal with is (x−7a)(3x−a) < 0 → a/3 < x < 7a