Chapter 1: Q30. (page 49)

Solve the equation and check the solution.
$\frac{n}{4} + \frac{n}{3} = \frac{1}{2}$

Short Answer

Expert verified

The solution is $n = \frac{6}{7}$ .

Step by step solution

Step 1- Consider the equation.

Consider the equation $\frac{n}{4} + \frac{n}{3} = \frac{1}{2}$ .

Multiply both sides of the equation by 12 and simplify.

Step 2- Step description.

$\begin{array}{l} \frac{n}{4} (12) + \frac{n}{3} (12) = \frac{1}{2} (12) \\ 3 n + 4 n = 6 \\ 7 n = 6 \end{array}$

Step 3- Step description.

Divide both sides of the equation by 7.

$\begin{array}{l} 7 n = 6 \\ n = \frac{6}{7} \end{array}$

Therefore, the solution is $n = \frac{6}{7}$ .

Step 4- Verify the solution.

Substitute $n = \frac{6}{7}$ in the equation and simplify as follows:

\begin{matrix} \frac{n}{4} + \frac{n}{3} = \frac{1}{2} \\ \frac{(\frac{6}{7})}{4} + \frac{(\frac{6}{7})}{3} = \frac{1}{2} \\ \frac{6}{7 \times 4} + \frac{6}{7 \times 3} = \frac{1}{2} \\ \frac{3}{14} + \frac{2}{7} = \frac{1}{2} \\ \frac{3 + 4}{14} = \frac{1}{2} \\ \frac{7}{14} = \frac{1}{2} \\ \frac{1}{2} = \frac{1}{2} \end{matrix}

Since the left-hand side of the equation is equal to the right-hand side of the equation, therefore, the solution is $n = \frac{6}{7}$ .

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Solve the equation and check the solution.
$\frac{n}{4} + \frac{n}{3} = \frac{1}{2}$

Short Answer

Step by step solution

Step 1- Consider the equation.

Step 2- Step description.

Step 3- Step description.

Step 4- Verify the solution.

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Solve the equation and check the solution.n4+n3=12

Short Answer

Step by step solution

Step 1- Consider the equation.

Step 2- Step description.

Step 3- Step description.

Step 4- Verify the solution.

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Most popular questions from this chapter

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Solve the equation and check the solution.
$\frac{n}{4} + \frac{n}{3} = \frac{1}{2}$