Chapter SH, Problem 1.14EP

To determine

To solve:the given equation.And check the solution.

Answer to Problem 1.14EP

  $c=-18$ .

Explanation of Solution

Given:

The given equationis $4\left(c-5\right)-2\left(3c+5\right)=6$ .

Calculation:

As the given equation is $4\left(c-5\right)-2\left(3c+5\right)=6$ .

Now, solve the given equation. Therefore,

  $\begin{array}{l}4\left(c-5\right)-2\left(3c+5\right)=6\left\{\text{given equation}\right\}\\ \Rightarrow 4c-20-6c-10=6\left\{\text{simplify}\right\}\\ \Rightarrow -2c-30+30=6+30\left\{\text{add 30 on both the sides}\right\}\\ \Rightarrow -2c=36\{\text{simplify}}\\ \therefore c=\frac{36}{-2}\{\text{divide both sides by }-2\text{}}\\ c=-18\end{array}$

Check:

  $\begin{array}{l}4\left(c-5\right)-2\left(3c+5\right)=6\\ 4\left(-18-5\right)-2\left(3\left(-18\right)+5\right)=6\{\text{substitutes }c=-18\}\\ 4\left(-23\right)-2\left(-54+5\right)=6\\ -92-2\left(-49\right)=6\\ -92+98=6\\ 6=6\end{array}$

Hence, the solution of the given equation is $c=-18$ .