What is the solution of 2(x - 5) + 4 = 30?
I miss these easy *** problems.... 2(x-5) +4 = 30 2(x-5) = 26 2x-10 = 26 2x = 36 X=18
What is the solution to: √2x+13 -5=x?
√(2x+13) - 5 = x √(2x+13) = x + 5 2x + 13 = (x + 5)^2 2x + 13 = x^2 + 10x + 25 x^2 + 8x + 12 = 0 (x + 2)(x + 6) = 0 x = -6, -2 x = -6, √(2(-6)+13) - 5 = -6 √1 - 5 = -6 -3 = -6 is not true x = -2, √2(-2)+13 - 5 = -2 √9 - 5 = -2 3 - 5 = -2 ==> x = -2
What is the solution set for |2x – 3| = 11?
You have two possibilities. 2x - 3 = 11 or -(2x - 3) = 11 2x - 3 = 11 2x = 14 x = 7 -(2x - 3) = 11 -2x + 3 = 11 -2x = 8 x = -4 x = -4 or x = 7
What is the solution to [math]|2x - 4| < x - 1 [/math]?
This question got 2 solutions.Here are those.|2x-4|
What are the number of real solutions of |x^2+4x+3|+2x+5=0?
|x²+4x+3| = x² + 4x +3 whenx² + 4x +3 >= 0 x(x+3) >=0 i.e when x <= -3 or when x >= 0.....(1)So the equation becomes x² + 4x +3 + 2x +5 = 0Which gives x = - 4 and x = - 2 But we can't take x = - 2 as it not satisfies equation 1So x = -4 Now |x² + 4x + 3| = -(x² + 4x + 3)When x² + 4x + 3 <0 i.e when -3 < x < 0.......(2)So the equation becomes -(x² + 4x + 3) + 2x+5 = 0 -x² -2x +2 = 0 x = √3 - 1 and x = -(√3+1)But only x = - (√3+1) satisfy equation 2 so there are two answersx = - 4 and x= - (√3 +1)
What is the general solution of xy'+3y=2x^5, y(2) =1?
The above ODE shows a linear equation which can be solved using Integration Factor Method.xy' +3y =2x^5Divide through by x(xy')/x +(3/x)y =(2x^5)/xy' +(3/x)y =2x⁴IF=e^[ln(3/x)]=3/xThus, IF=3/xIF.y=∫2x⁴.IF3y/x =∫(2x⁴ . 3)/x3y/x =∫6x³3y/x=(6x⁴)/4 +cApply the boundary condition.Put x=2 and y=13(1)/2 =6(2)/4 +c3/2 =12/4 +c3/2 =3 +cC=3/2 - 3C=(3-6)/2C=-3/2Thus, the solution becomes3y/x =(6x⁴/4) - (3/2)3y/x =(6x⁴ - 6)/412y=6x^5 - 6x12y=6x(x⁴ - 1)
Have many solutions does 2x=x+5? have?
I will assume that your question was “How many solutions does 2x=x+5 have?”, and the answer is: Only one. You can simplify the equation following this steps:[math]2x = x+5[/math][math]2x-x = 5[/math][math]x = 5[/math]
If x and y are natural numbers, then what is the solution of 2x+y=5?
Natural numbers are positive intgers. (Some people may include zero as Natural, but I usually don’t)Rearrange the equation and sub in values (in for x would be easier, but it doesn’t really matter)[math]2x+y=5[/math][math]y=5-2x[/math]Try [math]x=1[/math],[math]y=5-(2×1)[/math][math]y=5-2[/math][math]y=3[/math]so if [math]x=1[/math], then [math]y=3[/math]I’ll write these as coordinate pairs: [math](1,3)[/math]Then try [math]x=2,[/math][math]y=5-(2×2)[/math][math]y=5–4[/math][math]y=1[/math][math](2,1)[/math]If we try [math]x=3,[/math][math]y=5-(2×3)[/math][math]y=5–6[/math][math]y=-1[/math][math](3,-1)[/math]Here we have a problem since -1 is NOT a Natural Number, so this solution is invalid due to the restrictions imposed by the question.We also don’t need to go any higher with the [math]x[/math]-values, since it should be clear that we’ll just end up with more negative [math]y[/math]-valuesWe could have rearranged it to subsitute [math]y[/math] instead of [math]x[/math] into the equation:[math]2x+y=5[/math][math]2x=5-y[/math][math]x=(1/2)(5-y)[/math]Let’s sub in some values for [math]y[/math]:[math]y=1,[/math][math]x=(1/2)(5–1)[/math][math]x=(1/2)(4)[/math][math]x=2[/math][math](2,1)[/math]The same as we got when we used [math]x=2[/math][math]y=2,[/math][math]x=(1/2)(5-2)[/math][math]x=(1/2)(3)[/math][math]x=3/2[/math][math](3/2,3)[/math][math]3/2[/math] is NOT a Natural Number, so this is not a valid solution.[math]y=3,[/math][math]x=(1/2)(5-3)[/math][math]x=(1/2)(2)[/math][math]x=1[/math][math](1,3)[/math]Then try [math]y=4[/math][math]x=(1/2)(5-4)[/math][math]x=1/2[/math][math](1/2,4)[/math]This is not valid either since [math]1/2[/math] is NOT a Natural Number.Let’s try [math]y=5[/math][math]x=(1/2)(5-5)[/math][math]x=(1/2)(0)[/math][math]x=0[/math][math](0,5)[/math]And [math]x=0[/math][math]y=5-(2×0)[/math][math]y=5[/math][math](0,5)[/math]These last two may or may not be valid solutions depending on your (or your tutor’s) personal definition of a Natural NumberSo your possible solutions are:[math](0,5)[/math]?[math](1,3)[/math]and[math](2,1)[/math]
What is the solution set of the inequation (4x+3) / (2x-5) < 6?
As this involves numerator and denominator, it would be way hard to write it in that way. so I am uploading a click of my answer:Extremely sorry for my bad handwriting.I am writing the final answer to the question:x € (-∞,2.5) U (4.125,∞)