Question

3 ( x + 1 ) = 4 ( 3/5x + 3 )

Answer 1

Given the equation

`3(x+1)\text{ = 4(}(3)/(5)x\text{ +3)}`

Step 1

Open brackets by multiplying the terms in the brackets by the outer factors.

`3x\text{ + 3 = }(12)/(5)x\text{ +12}`

Step 2

Collect like terms.

`\begin{gathered} 3x-(12)/(5)x=12-3 \\ (3)/(5)x=8 \end{gathered}`

Step 3

Multiply both sides by 5, to remove the fraction.

`\begin{gathered} 5\text{ }*(3)/(5)x\text{ = 8 }*\text{ 5} \\ \Rightarrow3x=40 \end{gathered}`

Step 4

Divide both sides by the coefficient of x.

`\begin{gathered} \text{The coefficient of x is 3} \\ \text{Thus,} \\ (3x)/(3)=(8)/(3) \\ \Rightarrow x=(8)/(3) \end{gathered}`

Hence, the solution to the equation is

`x=(8)/(3)`