Question

Select the statement that describe a logical next step for solving this equation.

Question 5 options:


Multiply both sides by 1/12

add 3/4x to both sides by 1/12

Divide both sides by 15

Subtract 2/3x from both sides

Answer 1

Subtract 2/3x from both sides

Explanation:

`(3)/(4)x-7=(2)/(3)x+8` add 7 to both sides

`(3)/(4)x=(2)/(3)x+15`

Answer: subtract 2/3x from both sides

`(3)/(4)x-(2)/(3)x=15` multiply both sides by 12

`12\!\!\!\!\!\diagup^3\cdot(3)/(4\!\!\!\!\diagup_1)x-12\!\!\!\!\!\diagup^4\cdot(2)/(3\!\!\!\!\diagup_1)x=(12)(15)`

`(3)(3x)-(4)(2x)=180\\\\9x-8x=180\\\\x=180`

Answer 2

Subtract
`(2)/(3)x` from both sides

Explanation:

When we solve a one variable equation then we isolate variable in the right side of the equation,

Here, the given equation,

`(3)/(4)x-7=(2)/(3)x+8`

Adding 7 on both sides,

`(3)/(4)x=(2)/(3)x+15`

We need to isolate x in the right side,

So, we have to remove the term having x in the left side,

For this we need to subtract
`(2)/(3)x` on both sides,

Further steps are as follow,

`(3)/(4)x-(2)/(3)x=15`

`(9x-8x)/(12)=15`

`(x)/(12)=15\implies x = 180`