Question

All of the following equations have the same solution except _____.

-1.8 + x = -1.6
7.5 x = 1.5
x + 6.5 = 6.3
x/5 = 0.04

Answer 1

x + 6.5 = 6.3

Explanation:

Solve each equation for x:

`\begin{aligned}\textsf{Equation 1}: \quad \quad \quad -1.8+x&=-1.6\\-1.8+x+1.8&=-1.6+1.8\\x&=0.2\end{aligned}`

`\begin{aligned}\textsf{Equation 2}: \quad\quad \quad\quad \quad 7.5x&=1.5\\7.5x / 7.5&=1.5 / 7.5\\x&=0.2\end{aligned}`

`\begin{aligned}\textsf{Equation 3}: \quad \quad \quad \quad x+6.5&=6.3\\x+6.5-6.5&=6.3-6.5\\x&=-0.2\end{aligned}`

`\begin{aligned}\textsf{Equation 4}: \quad \quad \quad\quad \quad \quad(x)/(5)&=0.04\\(x)/(5) \cdot 5&=0.04\cdot 5\\x&=0.2\end{aligned}`

The solution for equations 1, 2 and 4 is x = 0.2.

The solution for equation 3 is x = -0.2.

Therefore, all of the equations have the same solution except:

• x + 6.5 = 6.3

Answer 2

• C) x + 6.5 = 6.3

Explanation:

Solve each equation and compare solutions.

• A) -1.8 + x = -1.6 ⇒ x = 1.8 - 1.6 ⇒ x = 0.2
• B) 7.5 x = 1.5 ⇒ x = 1.5/7.5 ⇒ x = 0.2
• C) x + 6.5 = 6.3 ⇒ x = 6.3 - 6.5 ⇒ x = - 0.2, this is different
• D) x/5 = 0.04 ⇒ x = 0.04*5 ⇒ x = 0.2