Question

How is solving $3\mathrm{x}-7=-5$different from solving$3\mathrm{x}+7=-5$?

Short answer

Solving equation $3x-7=-5$ requires addition of 7 to both sides of the equation first and solving $3x+7=-5$ requires subtraction of 7 from both sides of the equation first.

Step-by-step solution

– Solve the first equation

Solve the equation $3x-7=-5$.

$\begin{array}{l}3x-7=-5\\ 3x=-5+7\\ 3x=2\\ x=\frac{2}{3}\end{array}$

The solution of the equation is$x=\frac{2}{3}$.

– Solve the second equation 

Write the second equation and solve it.

$\begin{array}{l}3x+7=-5\\ 3x=-5-7\\ 3x=-12\\ x=\frac{-12}{3}\\ x=-4\end{array}$

Therefore, the solution of the equation is $x=-4$.

 Step 3 – Observation from equations 

To solve the $3x-7=-5$, one needs to add 7 to both sides of the equation first and for solving $3x+7=-5$, one needs to subtract 7 from both sides of the equation.

Thus, solving equation $3x-7=-5$requires addition of 7 to both sides of the equation first and solving $3x+7=-5$requires subtraction of 7 from both sides of the equation first.