Solve (5-x)(6+2x)=-2+4x Using the Distributive Property

Question

Solve the following equation using the distributive property:

(5x)(6+2x)=2+4x (5-x)(6+2x)=-2+4x

Video Solution

Step-by-Step Solution

To solve the given equation (5x)(6+2x)=2+4x (5-x)(6+2x)=-2+4x , we'll apply the following steps to use the distributive property:

  • Step 1: Expand the left side using the distributive property:
    (5x)(6+2x)=56+52xx6x2x (5-x)(6+2x) = 5 \cdot 6 + 5 \cdot 2x - x \cdot 6 - x \cdot 2x =30+10x6x2x2 = 30 + 10x - 6x - 2x^2 Finally, combine like terms:
    =2x2+4x+30 = -2x^2 + 4x + 30
  • Step 2: Set the equation against the right side:
    2x2+4x+30=2+4x -2x^2 + 4x + 30 = -2 + 4x
  • Step 3: Move all terms to one side of the equation:
    2x2+4x+304x(2)=0 -2x^2 + 4x + 30 - 4x - (-2) = 0 Simplify to:
    2x2+32=0 -2x^2 + 32 = 0
  • Step 4: Solve the quadratic equation:
    Factor out the common term:
    2(x216)=0 -2(x^2 - 16) = 0
    x216=0 x^2 - 16 = 0
  • Step 5: Solve for x x :
    x2=16 x^2 = 16
    x=±4 x = \pm 4

Therefore, the solution to the equation is x=±4 x = \pm 4 .

Answer

x=±4 x=±4