Question

Determine whether or not the two equations below have the same solution. In two or more complete sentences, explain your rationale

Answer 1

Answer:

Yes, they have the same solution.

Step-by-step explanation:

The steps in solving a two-step equation are to simplify by using

1. The inverse of addition or subtraction and then
2. The inverse of multiplication or division

Equation 1

$\dfrac{2}{3}x + \dfrac{3}{4} = 8$

(a) Inverse of addition

$\begin{array}{rcl}\dfrac{2}{3}x + \dfrac{3}{4} - \dfrac{3}{4}& = & 8 - \dfrac{3}{4}\\\\\dfrac{2}{3}x & = & \dfrac{29}{4}\\\end{array}$

(b) Inverse of multiplication

$\begin{array}{rcl}\left (\dfrac{2x}{3}\right ) \left (\dfrac{3}{2}\right ) & = & \left (\dfrac{29}{4}\right ) \left ( \dfrac{3}{2} \right ) \\\\x & = & \dfrac{87}{8}\\\end{array}$

Equation 2

8x = 87

(a) Inverse of multiplication

$\begin{array}{rcl}\dfrac{8x}{8} & = & \dfrac{87}{8}\\\\x & = & \dfrac{87}{8}\\\end{array}$

The two equations have the same solution.

For the first equation, I used the inverse of addition and then the inverse of multiplication to get the value of x.

The second equation needed only the inverse of multiplication.

Both solutions were the same.