Question

2x-1 over 5 equals 2+3x over 4

Answer 1

x = -2

Step-by-step explanation

We want to find x in the equation below:

`\frac{2x\text{ - 1}}{5}\text{ = }\frac{2\text{ + 3x}}{4}`

First, multiply both sides by 20, to eliminate both denominators:

`\begin{gathered} 20\cdot\text{ }(1)/(5)(2x\text{ - 1) = 20 }\cdot\text{ }(1)/(4)(2\text{ + 3x)} \\ \Rightarrow\text{ 4(2x - 1) = 5(2 + 3x)} \\ 8x\text{ - 4 = 10 + 15x} \\ \text{Collect like terms:} \\ 15x\text{ - 8x = -4 - 10} \\ 7x\text{ = -14} \\ x\text{ = }(-14)/(7) \\ x\text{ = -2} \end{gathered}`

That is the value of x.