Chapter 6.3, Problem 36E

To determine

To solve the equation and check the answer

Answer to Problem 36E

  $s=18$ is correct answer to the given equation $-6\left(s+7\right)=10\left(3-s\right)$

Explanation of Solution

Given information:

Equation $-6\left(s+7\right)=10\left(3-s\right)$ to solve

Concept used:

Use of BODMAS and solve the equations by rearranging like terms

Sign of terms changes while moving from left hand side of equation to right hand side of equation and vice versa.

Addition sign changes to subtraction and vice versa.

Multiply sign changes to division and vice versa.

Check answer by putting value of variable obtained on left hand side and right hand side, if both left hand side and right hand side are equal then the value obtained by solving the equation is correct.

Calculation:

  $\begin{array}{l}-6\left(s+7\right)=10\left(3-s\right)\\ -6s-42=30-10s\left(\text{open brackets }\right)\\ -6s+10s=30+42\left(\text{arrange like terms (variables on left side and constants on right)}\right)\\ 4s=72\\ s=\frac{72}{4}\\ s=18\end{array}$

Now to check answer solving left hand side and right hand side separately for s = 18

Left hand side

  $\begin{array}{l}-6\left(s+7\right)\\ \text{put }s=18\\ -6\left(s+7\right)=-6\left(18+7\right)=-6\left(25\right)=-150\end{array}$

Right hand side

  $\begin{array}{l}10\left(3-s\right)\\ \text{put }s=18\\ 10\left(3-s\right)=10\left(3-18\right)=10\times \left(-15\right)=-150\end{array}$

Since,

Left hand side = Right hand side

Therefore,

  $s=18$ is correct answer to the given equation $-6\left(s+7\right)=10\left(3-s\right)$