Question

Consider this equation:  2/3 x − 9 − 2x + 2 = 1

Which is an equivalent equation after combining like terms?

Answer 1

-4/3x (or -1 1/3x if you use whole numbers instead of an improper fraction) -7 = 1

Answer 2

`\displaystyle(2)/(3)x - 2x = 1 -2 + 9~~~~~~~~~~~~~~~~~~~~~~~~~~~(1)\\\\ (-4)/(3)x = 8~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(2)`

Explanation:

We are given the following information in the question:

We are given a equation:

`\displaystyle(2)/(3)x - 9 -2x + 2 = 1`

We have to write an equivalent equation to the given equation by combining the like terms.

Like terms:

• Like terms are terms that have the same variables and powers.
• The coefficients of the like terms do not need to match.
• Unlike terms are two or more terms that are not like terms, i.e. they do not have the same variables or powers.
• For example, 2x, 3x, 7x are examples of like terms.

Taking the like terms on one side, we can write the equation as:

`\displaystyle(2)/(3)x - 2x = 1 -2 + 9~~~~~~~~~~~~~~~~~~~~~~~~~~~(1)\\\\((2-6)/(3))x = 8\\\\(-4)/(3)x = 8~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(2)`

Equation (1) and (2) are equivalent equation obtained by combining like terms.