Question

Solve the equation using the justification given for each step.

Answer 1

`5x+7=((-15x-1))/(3)+(4)/(3)`

Multiplicative property of equality

`\begin{gathered} Multiply\text{ both sides by 3} \\ (5x+7)3=(3(-15x-1))/(3)+3((4)/(3)) \end{gathered}`

Distributive property of equality

`3(5x+7)=-15x-1+4`

Associative property

`\begin{gathered} 15x+21=-15x-1+4 \\ 15x+21=-15x+3 \end{gathered}`

Subtraction property of equality

`\begin{gathered} 15x+21-21=-15x+3-21 \\ 15x=-15x-18 \end{gathered}`

Addition property of equality

`\begin{gathered} 15x+15x=-15x+15x-18 \\ 30x=-18 \end{gathered}`

Division property of inequality

`\begin{gathered} \text{divide both sides by 30} \\ (-18)/(30)=(30x)/(30) \\ x=-(18)/(30)=-(3)/(5) \end{gathered}`