algebra question

algebra question

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There are five steps to solving simple algebraic equations

- Clear any fractions by multiplying all the terms on both sides of the equation by the denominators
- Remove all parentheses
- Transpose all of the terms containing the unknown variable to one side of the equation and all known numbers or variables on the other side of the equation
- Combine like terms on each side of the equation
- Divide both sides by whatever coefficient is in front of the unknown variable.

For our equation since we don't have fractions or parenthesis, we can begin with step 3 and using a
rule of algebra of **performing the inverse of a function** to move it from one side of the equation to the other. In order to move +6x to the left side of the equation, we will
*subtract* 6x from both sides. Likewise, to move the -4x to the left side, we will
*add* 4x to both sides. The same rule applies to the known variables.

8x + 7 - 3x = 6x + 19 - 4x now becomes

8x - 3x - 6x + 4x = 19 - 7

Next, reduce the complexity of the equation by combining like terms on each side of the equation

3x = 12

Lastly, remove the coefficient from the unknown term, again using the rule of performing the inverse of a function. The inverse of 3 is 1/3, so multiply both sides of the equation by 1/3. Or to state it another way, divide both sides by 3.

x = 4.

First combine terms with x's in them and combine the others to get:

5x + 7 = 2x + 19

Then subtract 2x from both sides and subtract 7 from both sides to get:

3x = 12