Question

Solve the equation for `x`:



`\frac{2}{5}\left(x+1\right)=g`

Answer 1

To solve the equation, let's first simplify the left side. We can do this by distributing the fraction `\frac{2}{5}` to each term inside the parentheses:

`\frac{2}{5}(x+1) = \frac{2}{5} \cdot x + \frac{2}{5} \cdot 1 = \frac{2x}{5} + \frac{2}{5}`

So the equation becomes:

\frac{2x}{5} + \frac{2}{5} = g

To isolate the variable `x`, we can subtract `\frac{2}{5}` from both sides of the equation:

\frac{2x}{5} = g - \frac{2}{5}

Next, we want to get rid of the fraction on the left side. We can multiply the entire equation by the reciprocal of `\frac{2}{5}`, which is `\frac{5}{2}`:

\frac{5}{2} \cdot \frac{2x}{5} = \frac{5}{2} \cdot \left(g - \frac{2}{5}\right)

The fraction on the left side cancels out, and we are left with:

x = \frac{5}{2} \cdot \left(g - \frac{2}{5}\right)

Multiplying through, we have:

x = \frac{5}{2} \cdot g - \frac{5}{2} \cdot \frac{2}{5}

Simplifying further, we get:

x = \frac{5}{2} \cdot g - 1

Therefore, the solution for `x` is:

x = \frac{5}{2} \cdot g - 1