Anonymous
Anonymous asked in Science & MathematicsMathematics · 4 weeks ago

3x (x+2)= 2 (x + 5) help solve this plz and also this equation 1/6 (x - 5 ) =1/2 (x + 6) ?

If possible plz explain how you got the answer because my teacher is really bad at teaching and don't want to ask her cuz she will be pissed that I didn't ask her earlier so plz help I don't want to fail math!!!!

6 Answers

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  • Como
    Lv 7
    4 weeks ago

    :-

    1.

    3x² + 6x = 2x + 10

    3x² + 4x - 10 = 0

    x = [ - 4 ± √( 16 + 120 ) ] / 6

    x = [ - 4 ± √136 ] / 6

    x = [ - 4 ± 2√34 ] / 6

    x. = [ - 2 ± √34 ] / 3

    2.

    x - 5 = 3 ( x + 6 )

    x = 3x + 23

    - 23 = 2x

    x. = - 23/2

  • 4 weeks ago

    Question 1:

    Distribute:

    3x²+6x=2x+10

    Subtract 10 from both sides:

    3x²+6x-10=2x+10-10

    Simplify:

    3x²+6x-10=2x

    Subtract 2x from both sides:

    3x²+6x-10-2x=2x-2x

    Simplify:

    3x²+4x-10=0

    Use the quadratic formula:

    x=[-2+√(34)]/3 or x=[-2-√(34)]/3

    Answer: x=[-2+√(34)]/3 or x=[-2-√(34)]/3

    Question 2:

    Distribute:

    1/6x-5/6=1/2x+3

    Add 5/6 to both sides:

    1/6x-5/6+5/6=1/2x+3+5/6

    Simplify:

    1/6x=1/2x+23/6

    Subtract 1/2x from both sides:

    1/6x-1/2x=1/2x+23/6-1/2x

    Simplify:

    -1/3x=23/6

    Multiply both sides by -3:

    x=-23/2

    Answer: -23/2

  • David
    Lv 7
    4 weeks ago

    Question 1) If you mean: 3x times (x+2) = 2 times (x+5) 

    Then: 3x^2 +6x = 2x+10)

    Transposing and collecting like terms: 3x^2 +4x -10 = 0

    Use the quadratic equation formula to solve for x:

    x = -(2 + square root 34)/3 or x = (-2 + square root 34)/3

    Question 2) If you mean: 1/6 times (x-5) = 1/2 times (x+6)

    Then: x/6 -5/6 = 0.5x +3

    Multiply all terms by 6: x -5 = 3x +18

    Or: x -3x = 18+5 => -2x = 23 

    Divide both sides by -2: x = -11.5

  • Ian H
    Lv 7
    4 weeks ago

    3x (x+2)= 2(x + 5)  

    3x^2 + 6x – 2x – 10 = 0 

    3x^2 + 4x – 10 = 0 

    Use the quadratic formula  

    x = [-2 ± √(34)]/3 

     

    Or complete the square like this 

    3x^2 + 4x – 10 = 0 

    x^2 + (4/3)x = 10/3 

    Add (half the coefficient of x) squared, to both sides 

    x^2 + (4/3)x + 4/9 = 4/9 + 30/9 

    (x + 2/3)^2 = 34/9 

    x + 2/3 = ±√(34)]/3 

    x = [-2 ± √(34)]/3 

     

    (x - 5 )/6 = (x + 6)/2  multiply both sides by 6 

    x – 5 = 3x + 18 

    -23 = 2x 

    x = -23/2 

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  • 4 weeks ago

    3x.(x + 2) = 2.(x + 5)

    3x² + 6x = 2x + 10

    3x² + 4x = 10

    x² + (4/3).x = 10/3

    x² + (4/3).x + (2/3)² = (10/3) + (2/3)²

    [x + (2/3)]² = 34/9

    [x + (2/3)]² = [± (√34)/3]²

    x + (2/3) = ± (√34)/3

    x = - (2/3) ± [(√34)/3]

    x = (- 2 ± √34)/3

    x₁ = (- 2 ± √34)/3

    x₂ = (- 2 ± √34)/3

    (1/6).(x - 5) = (1/2).(x + 6)

    (x - 5)/6 = (x + 6)/2

    2.(x - 5) = 6.(x + 6)

    2x - 10 = 6x + 36

    2x - 6x = 36 + 10

    - 4x = 46

    x = - 46/4

    x = - 23/2

  • 4 weeks ago

    3x (x+2)= 2 (x + 5)

    Expand on the left and right, separately:

    3x^2 + 6x = 2x + 10

    Combine like terms and write in standard form:

    3x^2 + 4x - 10 = 0

    Use the quadratic formula:

    x = (1/3) (-2 - √(34))

    x = (1/3) (-2 + √(34))

    1/6 (x - 5 ) =1/2 (x + 6)

    Multiply both sides by 6:

    x - 5 = 3 (x + 6)

    Expand on the right:

    x - 5 = 3x + 18

    Combine like terms:

    -2x = 23

    Divide both sides by -2:

    x = - 23/2

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