Question1) $7(2+7 n)=259$

Studdy Solution

STEP 1

1. The equation $7(2 + 7n) = 259$ is a linear equation in terms of $n$ .
2. The goal is to solve for $n$ .
3. The equation involves basic algebraic operations, including distribution and division.

STEP 2

1. Distribute the constant outside the parentheses.
2. Simplify the equation.
3. Isolate the variable $n$ by performing algebraic operations.
4. Check the solution by substituting it back into the original equation.

STEP 3

Distribute the $7$ across the terms inside the parentheses:
$7 \times 2 + 7 \times 7n = 259$
This simplifies to:
$14 + 49n = 259$

STEP 4

Subtract $14$ from both sides to begin isolating $n$ :
$49n = 259 - 14$
Simplify the right-hand side:
$49n = 245$

STEP 5

Divide both sides by $49$ to solve for $n$ :
$n = \frac{245}{49}$
Simplify the division:
$n = 5$

STEP 6

Check the solution by substituting $n = 5$ back into the original equation:
$7(2 + 7 \times 5) = 259$
Simplify inside the parentheses:
$7(2 + 35) = 259$
$7 \times 37 = 259$
Calculate the left-hand side:
$259 = 259$
Both sides are equal, confirming the solution is correct.
The solution is:
$\boxed{5}$

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