QuestionSolve using the addition principle. $2 \frac{1}{5}+x=7$

Studdy Solution

STEP 1

1. The equation $2 \frac{1}{5} + x = 7$ is asking us to solve for $x$ .
2. This is a one-step equation that can be solved using the addition principle.
3. The equation involves fractions and basic algebraic operations.

STEP 2

1. Convert the mixed number to an improper fraction.
2. Use the addition principle to isolate the variable $x$ .
3. Simplify to find the value of $x$ .
4. Check the solution by substituting it back into the original equation.

STEP 3

Convert the mixed number $2 \frac{1}{5}$ to an improper fraction.
$2 \frac{1}{5} = \frac{2 \times 5 + 1}{5} = \frac{11}{5}$

STEP 4

Rewrite the equation using the improper fraction:
$\frac{11}{5} + x = 7$

STEP 5

Use the addition principle to isolate $x$ . Subtract $\frac{11}{5}$ from both sides of the equation:
$x = 7 - \frac{11}{5}$

STEP 6

To subtract, convert 7 to a fraction with a denominator of 5:
$7 = \frac{35}{5}$
Now perform the subtraction:
$x = \frac{35}{5} - \frac{11}{5} = \frac{24}{5}$

STEP 7

Check the solution by substituting $x = \frac{24}{5}$ back into the original equation:
$2 \frac{1}{5} + \frac{24}{5} = 7$
Convert $2 \frac{1}{5}$ to $\frac{11}{5}$ and add:
$\frac{11}{5} + \frac{24}{5} = \frac{35}{5} = 7$
Both sides are equal, confirming the solution.
The solution is:
$\boxed{\frac{24}{5}}$

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