Question

How do you solve `\frac { 1} { 2} ( 2x - 6) + 5- \frac { 2} { 3} x + 9+ \frac { 7} { 3} x`?

Answer 1

You need to group and combine like terms.

Explanation:

First, let's distribute the `1/2`to the `2x-6`. Our new equation will be `x-3+5-(2/3)x+9+(7/3)x`. Now we can group our x's together, and since the common denominator is 3, our equation will be `3/3x-2/3x+7/3x-3+5+9` after grouping like terms together. After simplifying, our answer will be `8/3x+11`.

Answer 2

This expression simplifies to `(8x)/3+11`.

Explanation:

Simplify.

This is an expression, not an equation. So it can't be solved, but it can be simplified.

`1/2(2x-6)+5-2/3x+9+7/3x`

Simplify `2/3x` and `7/3x` to `(2x)/3` and `(7x)/3`.

`1/2(2x-6)+5-(2x)/3+9+(7x)/3`.

Simplify `1/2(2x-6)` to `(2x-6)/2`.

`(2x-6)/2+5-(2x)/3+9+(7x)/3`

Simplify `(2x-6)/2` to `(2(x-3))/2`

`(2(x-3))/2+5-2/3x+9+7/3x`

Simplify `(2(x-3))/2` to `(x-3)`.

`x-3+5-2/3x+9+7/3x`

`x-3+5-(2x)/3+(7x)/3`

Gather like terms.

`(x-3)+(5+9)+(-(2x)/3+(7x)/3)`

Simplify.

`x-3+14+(5x)/3`

Collect like terms.

`(x)+(-3+14)+(5x)/3`

Simplify.

`x-11+(5x)/3`

Multiply `x/1` and `11/1` by `3/3` to make all denominators the same.

`x/1xx3/3+11xx3/3+(5x)/3`

Simplify.

`(3x)/3+(5x)/3+33/3`

Combine.

`(8x)/3+33`

Simplify.

`1/3(8x+33)`

Simplify.

`(8x)/3+11`