Chapter 1: Q63. (page 32)

Solve the equation and check the solution.
$\frac{5}{7} y - 3 = \frac{3}{7} y + 1$

Short Answer

Expert verified

The solution is $y = 14$ .

Step by step solution

Step 1- Consider the equation.

Consider the equation $\frac{5}{7} y - 3 = \frac{3}{7} y + 1$ .

Multiply both sides of the equation by 7.

$\begin{matrix} \frac{5}{7} y - 3 = \frac{3}{7} y + 1 \\ 7 \times \frac{5}{7} y - 3 (7) = 7 \times \frac{3}{7} y + 1 (7) \\ 5 y - 21 = 3 y + 7 \end{matrix}$

Step 2- Step description.

Now, simplify the equation obtained as follows:

$\begin{matrix} 5 y - 21 = 3 y + 7 \\ 5 y - 3 y = 7 + 21 \\ 2 y = 28 \end{matrix}$

Step 3- Step description.

Divide both sides of the equation by 2.

$\begin{array}{l} 2 y = 28 \\ y = \frac{28}{2} \\ y = 14 \end{array}$

Therefore, the solution is $y = 14$ .

Step 4- Verify the solution.

Substitute $y = 14$ in the equation and simplify as follows:

$\begin{matrix} \frac{5}{7} y - 3 = \frac{3}{7} y + 1 \\ \frac{5}{7} (14) - 3 = \frac{3}{7} (14) + 1 \\ \frac{70}{7} - 3 = \frac{42}{7} + 1 \\ \frac{70 - 21}{7} = \frac{42 + 7}{7} \\ \frac{49}{7} = \frac{49}{7} \\ 7 = 7 \end{matrix}$

Since the left-hand side of the equation is equal to the right-hand side of the equation, therefore, the solution is $y = 14$ .

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Solve the equation and check the solution.
$\frac{5}{7} y - 3 = \frac{3}{7} y + 1$

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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Short Answer

Step by step solution

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Solve the equation and check the solution.
$\frac{5}{7} y - 3 = \frac{3}{7} y + 1$