# 6(4 +2x) = 4(2x-1) + 4(x + 3)?

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Hi there --

Two things to keep in mind in this problem. Making sure that you properly distribute your quantities, and knowing what to do when you end up with a "solution" that is a contradiction -- which we end up getting in this problem. Whenever we reduce an equation to a contradiction (i.e. 4 = 12, 2 = -1, 0 = 1, etc.) it means there is no solution to the equation. Here's how we end up with one:

6(4 + 2x) = 4(2x - 1) + 4(x + 3)

6∙4 + 6∙2x = 4∙2x - 4∙1 + 4∙x + 4∙3

24 + 12x = 8x - 4 + 4x + 12

24 + 12x = 12x + 8

24 + 12x - 24 = 12x + 8 - 24

12x = 12x - 16

12x - 12x = 12x - 12x - 16

0 = -16

which is the contradiction. Which means this equation has no solutions.

I put together a short video tutorial walk-through of a solution to your question, and listed it below as well. Hope it's helpful!

• 6(4 +2x) = 4(2x-1) + 4(x + 3) <= original equation

24 + 12x = 8x - 4 + 4x + 12 <= simplify by distribution

24 + 12x = 12x + 8 <= combine like terms on right side of equation (the x's - just add them together)

24 ≠ 8 <= subtract 12x from both sides; 24 does not equal 8

Now, when the result is two numbers that clearly do not equal each other, this is considered "no solution," or no valid solution for x. If, for example, you were left with 8 = 8, this is considered to be "all real numbers," meaning x can equal all real numbers, so x has an infinite numbers of answers!

Hope this helps! :-)

Source(s): Honors Algebra II/Trig Student
• 6(4 +2x) = 4(2x-1) + 4(x + 3)

24 + 12 x = 8 + 12 x

No Solution

• 6(4+2x)=4(2x-1)+4(x+3),

24+12x=8x-4+4x+12,

24+12x=12x-4+12,

24+12x=12x+8,

24=12x-12x+8,

24=8, no solution.

• 6(4 + 2x) = 4(2x - 1) + 4(x + 3)

24 + 12x = 8x - 4 + 4x + 12

12x - 8x - 4x = -4 + 12 - 24

0 = -16

False.

• I got -0.8 though I could be wrong.

Use the five finger steps:

1.) Get rid of paranthesis <distribute>

2.) Combine like terms

3.) Get variable on one side

4.) Get constant on other side (+ or -)

5.) Divide by coefficient (* or ÷)

P.S. When solving equations like these, it would be opposite.