Q35.

Solve each equation. Check your solution.

$3.2 k - 4.3 = 12.6 k + 14.5$

Verified

Answer

The solution of the given equation is $k = - 2$ .

1Step 1. Write the given equation.

The given equation is “ $3.2 k - 4.3 = 12.6 k + 14.5$ ”.

2Step 2. Solve the given equation.

Solving,

$3.2 k - 4.3 = 12.6 k + 14.5$ (Given equation)

$3.2 k - 4.3 - 12.6 k = 12.6 k + 14.5 - 12.6 k$ (Subtract $12.6 k$ from both sides)

$- 9.4 k - 4.3 = 14.5$ (Simplify)

$- 9.4 k - 4.3 + 4.3 = 14.5 + 4.3$ (Add $4.3$ to both sides)

$- 9.4 k = 18.8$ (Simplify)

$\frac{- 9.4 k}{- 9.4} = \frac{18.8}{- 9.4}$ (Divide both sides by $- 9.4$ )

$k = - 2$ (Simplify)

So, $k = - 2$ is the solution of the given equation.

3Step 3. Check the obtained solution.

Put $k = - 2$ in the given equation $3.2 k - 4.3 = 12.6 k + 14.5$ to get,

$\begin{array}{l} 3.2 (- 2) - 4.3 = 12.6 (- 2) + 14.5 \\ - 6.4 - 4.3 = - 25.2 + 14.5 \\ - 10.7 = - 10.7 \end{array}$

Since the value obtained on the left-hand side and right-hand side are equal, the obtained value is indeed a solution of the given equation.