Question

HURRY I'LL PICK A BRAINLIEST PERSON!!!

Answer 1

The answer is A,B,&D.

Answer 2

Answer:

The only options which are having same solution as the given equation is A, B and D.

Explanation:

Given the equation: $\frac{3}{5}x+ \frac{2}{3} +x =\frac{1}{2}- \frac{1}{5}x$ ......[1]

Like terms are terms whose variables are the same.

In the given equation [1],

Combine like terms of variable x on LHS; we have

$\frac{3x+5x}{5}+ \frac{2}{3} =\frac{1}{2}- \frac{1}{5}x$

Simplify:

$\frac{8x}{5}+\frac{2}{3} =\frac{1}{2}- \frac{1}{5}x$

or we can write this as;

$\frac{8}{5}x +\frac{2}{3} =\frac{1}{2}- \frac{1}{5}x$ .

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

Taking LCM to both sides of an equation [1] as;

LCM of 3, 5 on LHS is 15 and LCM of 2 , 5 on RHS is 10;

$\frac{9x+10+15x}{15} = \frac{5-2x}{10}$

By cross multiplication we get;

$10 \cdot (9x+10+15x) = 15 \cdot (5-2x)$

Divide both side by 5 we get;

$2 \cdot (9x+10+15x) = 3 \cdot (5-2x)$

Using distributive property on both sides of an equation (i.e,   $a\cdot (b+c) =a\cdot b+a\cdot c$ )

we have;

$18x+20+30x = 15-6x$                 ......[2]

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

Using additive property of equality:

Add 6x to both sides of an equation in [2];

$18x+20+30x+6x = 15-6x+6x$  

Simplify;

$18x+20+30x+6x = 15$  

Combine 18x and 6x  we get;

$24x+20+30x= 15$                      ......[3]

Subtraction Property of Equality states that allows one to subtract the same quantity to both sides of an equation.

Subtract 20 from both sides of an equation in [3] we get;

$24x+20+30x-20= 15-20$

Simplify:

$24x+30x= -5$

Therefore, from the given options only A, B and D have the same solution as $\frac{3}{5}x+ \frac{2}{3} +x =\frac{1}{2}- \frac{1}{5}x$