(A): 4x + y = 7 (B): 2x - 3y = -7 2*(B) 4x - 6y = -14 Subtract from (A) 7y = 21 Divide both sides by 7: y = 3 Substitute in (A): 4x + 3 = 7 ie 4x = 4 or x = 1 Answer: x = 1 , y = 3
12x2 + 7x + 1 = 12x2 + 3x + 4x + 1 = 3x*(4x + 1) + 1*(4x + 1) = (4x + 1)*(3x + 1)
7
You would probably use a power-reduction trig identity to solve this equation. This states that sin2(x) = (1 - cos(2x))/2 Therefore, sin2(2x) = (1 - cos(4x))/2, or (1/2)(1 - cos(4x)) So, ∫ (1/2)(1 - cos(4x)) dx = (1/2) ∫ (1 - cos(4x)) dx. Then, ∫ (1-cos4x)dx = x - (1/4)sin(4x) + c Now, multiply that by (1/2) to get: (x - (sin(4x)/4) + c)/2 Since c is an arbitrary constant, we have: ½(x - sin(4x) / 4) + c OR 1/8 * (4x - sin(4x)) + c
4x+6x=30 is the same as: 10x=30 so we divide by 10 and get: x=3 (I do not see how this relates to calculus, but O.K.)
4x - 1 = 7 Add 1 to both sides: 4x = 8 Divide both sides by 4: x = 2
4x - 1 = 9(+ 1 on both sides)4x = 10(Divide both sides by 4)x = 2.5
-1 = 3 + 4x take 3 away from both sides: -4 = 4x divide both sides by 4 -1 = x
0.5
4x = 72.divide both sides by 4x = 18
you want to put all of the 'x' on one side and all of the numbers on the other side 2x-5=4x-1 2x-5 (-2x +1) = 4x -1 (-2x + 1) -4 = 2x then divide by 2 x=-2
4x-9=k 4x=k+9 Divide by 4 to isolate the x x=(1/4)k+(9/4) x=1/4 k+ 9/4
Solve for x 3-4x=5x-6 Subtract 5x from both sides to get 3-4x-5x=-6 Subtract 3 from both sides to get -4x-5x=-6-3 Combine like terms on each side to get -9x=-9 Divide each side by -1 to get 9x=9 Divide each side by 9 to get x=1 Answer x=1
4x = 20 x = 5 (divide both sides by 4)
2y = 4x - 2 Divide each side by 2: y = 2x - 1 In this form, you can see that the line has a slope of 2 and a y-intercept of -1 .
4x - 7 + 3 = 0 Combine like terms: 4x - 4 = 0 Add 4 to both sides: 4x = 4 Divide both sides by 4: x = 1
Divide all terms by 2 and when factored it is: (x+1)(x+1)