Use properties to rewrite the given equation. which equations have the same solution as 3/5x +2/3 + x = 1/2– 1/5x? check all that apply. a. 8/5x+2/3=1/2-1/5x b. 18x + 20 + 30x = 15 – 6x c. 18x + 20 + x = 15 – 6x d. 24x + 30x = –5 e. 12x + 30x = –5

Only options a ,b,d have the same solution as

Step-by-step explanation:

Given:

An equation:      ....[1]

Like terms states that contain the same variables raised to the same power.

Combine like terms on left hand side in equation [1] we get,

we get option (a) as the same solution.

Using LCM(Least Common ) to change each fraction to make their denominators the same as the least common denominator

Taking LCM both sides in Equation (1) ,

As LCM(3,5)=15 and LCM(2,5)=10 we have,

On simplifying we get,

=

Dividing both sides by 5 we get,

On simplify:

∴

which is same solution as given in option (b).

Now,

Use Additive Property of Equality states that allows one to add the same quantity to both sides of an equation.

Further, using the above property add 6x both sides  in   we get,

On simplifying we get,

Subtract 20 from both the sides we get,

Simplify:

or, which is same solution  as given in option(d)

But, options c and e equation doesn't have same solution as

hey there!

if she's saving for six months, let's divide the total number we need for the trip by six, dividing it into the amount that needs to be saved for each month.

500 ÷ 6 =

she needs to save at least this amount each month, so we should use this symbol: ≥

let x be the amount she saves each month.

your final answer is x ≥

hope this !