Question

For which equation would x = 0 be a solution?4 x = -46 x = 1\6(7 3\8 ) x = 01,000 x = 0.001

Answer 1

To determine the equation which will give

`x=0`

as a solution, we will solve through the given options.

Thus,

`\begin{gathered} 4x=-4 \\ divide\text{ both sides by the coefficient of x, which is 4} \\ (4x)/(4)=-(4)/(4) \\ \Rightarrow x=-1 \end{gathered}`
`\begin{gathered} 6x=(1)/(6) \\ multiply\text{ through by 6,} \\ 6(6x)=6((1)/(6)) \\ \Rightarrow36x=1 \\ divide\text{ both sides by the coefficient of x, which is 36} \\ (36x)/(36)=(1)/(36) \\ \Rightarrow x=(1)/(36) \end{gathered}`
`\begin{gathered} 7(3)/(8)x=0 \\ convert\text{ the mixed fraction to an improper fraction,} \\ (59)/(8)x=0 \\ divide\text{ both sides by the coefficient of x, which is }(59)/(8) \\ ((59)/(8)x)/((59)/(8))=(0)/((59)/(8)) \\ \Rightarrow x=0 \end{gathered}`
`\begin{gathered} 1000x=0.001 \\ divide\text{ both sides by the coefficient of x, which is 1000} \\ (1000x)/(1000)=(0.001)/(1000) \\ \Rightarrow x=1*10^(-6) \end{gathered}`

Hence, the equation that would give a solution of x=0, is

`7*(3)/(8)x=0`