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!!!!

Relevance
• :-

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

• 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

x=[-2+√(34)]/3 or x=[-2-√(34)]/3

Question 2:

Distribute:

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

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

• 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

• 3x (x+2)= 2(x + 5)

3x^2 + 6x – 2x – 10 = 0

3x^2 + 4x – 10 = 0

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

• 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

• 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

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