Question

Part BWhat should you do to get the two terms with variables on the left side of the equation?

Answer 1

Equation to be analyzed: 3/4t - 16 = 4/3t - 6

The question at the end says, "What should you do to get the two terms with variables on the left side of the equation?

In the above equation, our variable there is t. From the equation, we can see that the terms that have the variable t are 3/4t and 4/3t.

Since 3/4t is already on the left side, we will not do anything on that. Instead, we will transfer 4/3t to the left side by subtracting 4/3t on both sides of the equation to make it equal still as shown below.

`\begin{gathered} (3)/(4)t-16=(4)/(3)t-6 \\ (3)/(4)t-16-(4)/(3)t=(4)/(3)t-6-(4)/(3)t \\ (3)/(4)t-16-(4)/(3)t=-6 \end{gathered}`

Looking at the final equation, we can see that we already have the two terms with the variable t on the left side however, included on the left side of the equation is also the constant term -16. For us to eliminate -16 on the left side, we should add 16. So, to make it equal still, we will be adding 16 on both sides of the equation.

`\begin{gathered} (3)/(4)t-16-(4)/(3)t=-6 \\ (3)/(4)t-16-(4)/(3)t+16=-6+16 \\ (3)/(4)t-(4)/(3)t=10 \end{gathered}`

Finally, we only now have the two terms with variable t on the left side of the equation.

Therefore, to get the two terms with variables on the left side of the equation, we should subtract 4/3t and add 16 on both sides of the equation.