Question

Jada says, "I can tell that -2/3 (x+5)+4(x+5-10/3 (x+5) equals 0 just by looking at it. Is Jada correct? Explain how you know. I know its yes I just don't know how to explain it...Help!

Answer 1

Jada is correct.

Explanation:

Given equation is as follows,

`-(2)/(3)\left(x+5\right)+4\left(x+5\right)-(10)/(3)\left(x+5\right)=0`

In this case prove that right side of equation is equal to left side of equation.

Now consider left side of the equation,

`-(2)/(3)\left(x+5\right)+4\left(x+5\right)-(10)/(3)\left(x+5\right)`

Factoring out the common term,

`\left(x+5\right)\left(-(2)/(3)+4-(10)/(3)\right)`

Combining the like terms,

`\left(x+5\right)\left(-(2)/(3)-(10)/(3)+4\right)`

Since denominators of first terms are same, so combine the fractions.

`\left(x+5\right)\left((-2-10)/(3)+4\right)`

`\left(x+5\right)\left((-12)/(3)+4\right)`

Divide the number,

`\left(x+5\right)\left(-4+4\right)`

Subtracting,

`\left(x+5\right)\left(0\right)=0`

Hence left side of the equation is equal to 0 which is equal to right side of the equation.

Hence Jada saying is correct.