Question

How do I go about solving 2(7x+4)=4x-6(2-x) + 7

Answer 1

`\displaystyle x=-(13)/(4)`

Explanation:

Using the properties of equality, we can solve for a variable.

Solving for x

To solve for a variable we need to isolate it from any constants. There are multiple ways to begin solving, I will show the way I believe is easiest.

First, distribute the values outside the parentheses.

• 14x + 8 = 4x - 12 + 6x + 7

Then, combine like terms.

• 14x + 8 = 10x - 5

Next, subtract 10x from both sides.

• 4x + 8 = -5

Subtract 8 from both sides.

• 4x = -13

Finally, divide both sides by 4.

• 
  `\displaystyle x=-(13)/(4)`

This means x must equal -13/4 (-13/5 is also equivalent to -3.25).

Checking the Answer

To make sure we are right, we can plug our answer back into the original equation.

• 
  `\displaystyle 2(7(-(13)/(4)) +4)=4(-(13)/(4))-6(2-(-(13)/(4))) + 7`

Then, use arithmetic to solve this equation.

• 
  `\displaystyle -(75)/(2)= -(75)/(2)`

Since this equation is true, -13/4 must be the correct answer.