Question

Evaluate the following equation and check the solution is correct or not:

$3+g=\frac{1}{4}$

Short answer

The solution of the equation $3+g=\frac{1}{4}$is $g=-\frac{11}{4}$.

Step-by-step solution

Step 1. Given information.

The given equation is $3+g=\frac{1}{4}$.

Step 2. Write the concept.

In an equation, the variable represents the number that satisfies the equation.

To solve an equation means to find the value of the variable that makes the equation true.

If an equation is true and the same number is added to each side of the equation, then the resulting equivalent equation is also true.

Step 3. Solve the equation.

The equation $3+g=\frac{1}{4}$can be solved below:

$3+g=\frac{1}{4}$

Subtract 3 from both sides of the equation.

role="math" localid="1642409654291" $$\begin{gathered} 3+g-3=\frac{1}{4}-3 \\ g=\frac{1-3\times 4}{4} \end{gathered}$$

So,

$$\begin{gathered} g=\frac{1-12}{4} \\ =-\frac{11}{4} \end{gathered}$$

Step 4. Check the solution.

Take the equation $3+g=\frac{1}{4}$.

Substitute $g=-\frac{11}{4}$on the right-hand side of the equation.

role="math" localid="1642409827608" $$\begin{gathered} 3+g=\frac{1}{4} \\ 3+\left(-\frac{11}{4}\right)=\frac{1}{4} \\ 3-\frac{11}{4}=\frac{1}{4} \\ \frac{3\times 4-11}{4}=\frac{1}{4} \\ \frac{1}{4}=\frac{1}{4} \end{gathered}$$

This shows that, $g=-\frac{11}{4}$is the solution of the given equation.