Well, to answer your question,
Set up your equation 28/x = 112/100 (that's 28 divided by x = 112 divided by 100). Then you can cross-multiply (giving you 2800 = 112x) and solve for x (which in this case is 25).
Let the first even number = 2x. Then the preceding even number is 2x-2.(2x)/(2x-2) = 1.12x = 2.2x - 2.22x + 2.2 = 2.2x2.2 = 0.2x1.1 = 0.1 xx = 112x = 22The first even number is 22.The preceding even number is 20.22/20 = 1.1 yay!Since the question has some potential ambiguity in the wording, I offer an alternate interpretation to show why the answer above must be the correct interpretation. Perhaps it mean an even number is divided by the number preceding it.For example, if the number is 20, the one preceding it is 19 and of course not even.In this case the problem is (2x)/(2x-1) =1.12x=(2x-1)(1.1)2x=2.2x -1.1-.2x=-1.1x=1.1/.2or 11/2but then 2x =11 and this is not even so this interpretation does not work.So the first answer is the only interpretation that gives a valid answer.If fact I did not even need to do the algebra. An even number divided by an even number results in an odd number and an even number divided by an odd number results in a an even number. This would be used immediately to see which interpretation is correct. It only requires a little multiplication of the number by 10's so see that.
The equation 6 x-1 18x can be simplified to the answer 112x.
5x+33=112x-51, deduct 5x from each side of the equation leaves 33=107x-51, add 51 to each side leaves 84=107x, divide both sides by 107 gives answer x=84/107
8x-17=6x+112x=28x=14
Set up your equation 28/x = 112/100 (that's 28 divided by x = 112 divided by 100). Then you can cross-multiply (giving you 2800 = 112x) and solve for x (which in this case is 25).
72x-3=112x=14x=7
First of all, you don't factor an equation. You factor an expression.Next, here is a linear expression that can be factored: [ 96x + 4 ]. The factored form is: 4(24x + 1).Here is a third degree expression: [ 7x3 - 112x ]. The factored form is: 7x (x + 4) (x - 4).
7/8x -4 = 10 Multiply all terms by 8x: 7 -32x = 80x Add 32x to both sides 7 = 112x Divide both sides by 112 to find the value of x: x = 7/112 = 1/16
The solutions are x = 5, y = -9 and x = -2, y = 5.To solve:x2 - xy - y2 = -112x + y = 1Rearrange (2) to make y = 1 - 2x and substitute into (1):x2 - xy - y2 = -11⇒ x2 - x(1 - 2x) - (1 - 2x)2 = -11⇒ x2 - x + 2x2 - 1 + 4x - 4x2 = -11⇒ x2 - 3x - 10 = 0⇒ (x - 5)(x + 2) = 0⇒ x = 5 giving y = -9 (using x = 5 in equation (1) to find y)or x = -2 giving y = 5 (using x = -2 in equation (1) to find y)
3x - 11 = x + 5subtract x from both sides:3x - x - 11 = x - x +52x - 11 = 5add 11 to both sides:2x - 11 + 11 = 5+112x = 16divide both sides by 2 to solve for x:2x/2 = 16/2x = 8
112x9y9 128x2y7 -80x7y2 The GCF is 16x2y2
The two equations are:x² - xy - y² = -112x + y = 1The easiest way is to eliminate one of the unknowns by rearranging (2) so that y can be expressed as function of x, substituting this into (1) which will give a quadratic involving only x which can then be solved. (Alternatively rearranging 2 to express x in terms of y and then substituting for x in (1) can be done, but this leads to fractions which are not so easy to work with.) Once the values of x have been found, equation (2) can be used to find the corresponding values of y.Rearranging (2) to make y the subject gives y = 1 -2xSubstituting this for y in (1) gives:x² - x(1 - 2x) - (1 - 2x)² = -11→ x² - x + 2x² - (1 - 4x + 4x²) = -11→ 3x² - x - 1 + 4x - 4x² = -11→ -x² + 3x - 1 = -11→ x² - 3x - 10 = 0→ (x - 5)(x + 2) = 0→ x = 5 or -2Using (2) this gives:x = 5 → y = 1 - 2×5 = -9x = -2 → y = 1 - 2×-2 = 5→ The solutions are the points (5, -9) and (-2, 5)
Let the first even number = 2x. Then the preceding even number is 2x-2.(2x)/(2x-2) = 1.12x = 2.2x - 2.22x + 2.2 = 2.2x2.2 = 0.2x1.1 = 0.1 xx = 112x = 22The first even number is 22.The preceding even number is 20.22/20 = 1.1 yay!Since the question has some potential ambiguity in the wording, I offer an alternate interpretation to show why the answer above must be the correct interpretation. Perhaps it mean an even number is divided by the number preceding it.For example, if the number is 20, the one preceding it is 19 and of course not even.In this case the problem is (2x)/(2x-1) =1.12x=(2x-1)(1.1)2x=2.2x -1.1-.2x=-1.1x=1.1/.2or 11/2but then 2x =11 and this is not even so this interpretation does not work.So the first answer is the only interpretation that gives a valid answer.If fact I did not even need to do the algebra. An even number divided by an even number results in an odd number and an even number divided by an odd number results in a an even number. This would be used immediately to see which interpretation is correct. It only requires a little multiplication of the number by 10's so see that.