How do you solve #2(2+3)+4x=2(2x+2)+6#?

Question

Ethan Adkins · Accepted Answer

All real numbers or #(-oo, oo)# in interval notation.

#2(2+3) + 4x = 2(2x+2) + 6#

First, simplify #2(2+3)#:
#color(blue)(2(2+3) = 2(5) = 10)#

Put it back into the equation:
#10 + 4x = 2(2x+2) + 6#

Next, use the distributive property to simplify #2(2x+2)#:

Following this image, we know that:
#color(blue)(2(2x+2) = (2 * 2x) + (2 * 2) = 4x + 4)#

Put it back into the equation:
#10 + 4x = 4x + 4 + 6#

Add #4+6 = 10#:
#10 + 4x = 4x + 10#

Subtract #color(blue)(4x)# from both sides of the equation:
#10 + 4x quadcolor(blue)(-quad4x)= 4x + 10 quadcolor(blue)(-quad4x)#

#10 = 10#

Oh no! Our variables are gone now. Now we see if this equation is true. It is true that #10 = 10#, meaning that the answer is All real numbers or #(-oo, oo)# in interval notation.

Hope this helps!

Jace Anderson · Answer

undefined To solve the equation 2(2+3)+4x=2(2x+2)+6, follow these steps:

1. Start by simplifying both sides of the equation:
   2(2+3) + 4x = 2(2x+2) + 6
   2(5) + 4x = 2(2x+2) + 6
   10 + 4x = 4x + 4 + 6

2. Combine like terms on each side of the equation:
   10 + 4x = 4x + 10

3. Subtract 4x from both sides to eliminate the variable term on the right side:
   10 = 10

Since both sides of the equation are equal, this equation is an identity. This means that the equation is true for all values of x.

Kennedy Adams · Answer

undefined To solve the equation $ 2(2 + 3) + 4x = 2(2x + 2) + 6 $, you follow these steps:

1. First, simplify both sides of the equation by performing the operations within the parentheses.
2. Then, simplify the expressions involving multiplication and addition on both sides.
3. Next, combine like terms on each side of the equation.
4. Finally, isolate the variable $ x $ to solve for its value.

Let's solve it step by step:

1. $ 2(2 + 3) + 4x = 2(2x + 2) + 6 $
   Simplify inside the parentheses:
   $ 2(5) + 4x = 2(2x) + 2(2) + 6 $

2. $ 2(5) + 4x = 2(2x) + 2(2) + 6 $
   Perform multiplication:
   $ 10 + 4x = 4x + 4 + 6 $

3. $ 10 + 4x = 4x + 4 + 6 $
   Combine like terms on each side:
   $ 10 + 4x = 4x + 10 $

4. $ 10 + 4x = 4x + 10 $
   Notice that the terms $ 4x $ are on both sides of the equation. Subtract $ 4x $ from both sides to isolate $ x $:
   $ 10 = 10 $

After performing these steps, you'll notice that the equation $ 10 = 10 $ holds true. This indicates that no matter what value $ x $ takes, the equation remains true. Therefore, the solution to the equation is $ x $ can be any real number. In other words, it has infinite solutions.