Questions: Solve the following equation for x : 11x/5 - 4/5 = 1/5 Select the correct answer below: 4/11 20/11 10/11 1/11 -5/11 5/11

Transcript text: Question Solve the following equation for $x$ : \[ \frac{11 x}{5}-\frac{4}{5}=\frac{1}{5} \] Select the correct answer below: $\frac{4}{11}$ $\frac{20}{11}$ $\frac{10}{11}$ $\frac{1}{11}$ $-\frac{5}{11}$ $\frac{5}{11}$ FEEDBACK MORE

Solution

Solution Steps

To solve the equation $\frac{11 x}{5} - \frac{4}{5} = \frac{1}{5}$, we can follow these steps:

Eliminate the fractions by multiplying every term by 5.
Simplify the resulting equation.
Solve for $x$.

Step 1: Eliminate the Fractions

Multiply every term by 5 to eliminate the fractions: \[ 5 \left( \frac{11x}{5} - \frac{4}{5} \right) = 5 \left( \frac{1}{5} \right) \] This simplifies to: \[ 11x - 4 = 1 \]

Step 2: Simplify the Equation

Add 4 to both sides of the equation to isolate the term with $x$: \[ 11x - 4 + 4 = 1 + 4 \] This simplifies to: \[ 11x = 5 \]

Step 3: Solve for $x$

Divide both sides by 11 to solve for $x$: \[ x = \frac{5}{11} \]