Follow the steps to solve the following equation for [tex]\( x \)[/tex].

[tex]\[ \frac{1-3x}{5} = -7 \][/tex]

What should be subtracted from both sides to isolate the [tex]\( x \)[/tex]-term?

[tex]\[
\begin{array}{rr}
1 - 3x = -35 \\
-[?] & 1 - [?] \\
\hline
\end{array}
\][/tex]



Answer :

To solve the equation [tex]\(\frac{1 - 3x}{5} = -7\)[/tex], follow these steps:

1. Multiply both sides of the equation by 5 to eliminate the fraction:

[tex]\[ 5 \cdot \left(\frac{1 - 3x}{5}\right) = 5 \cdot (-7) \][/tex]

Simplifying this, we get:

[tex]\[ 1 - 3x = -35 \][/tex]

2. Subtract 1 from both sides to isolate the term with [tex]\(x\)[/tex]:

[tex]\[ 1 - 3x - 1 = -35 - 1 \][/tex]

Simplifying this, we get:

[tex]\[ -3x = -36 \][/tex]

3. Thus, the quantity that should be subtracted from both sides to isolate the [tex]\(x\)[/tex]-term is 1.

So the step-by-step solution shows that:

[tex]\[ \begin{array}{rr} 1 - 3x = -35 \\ -1 & \quad 1 - 1 \\ \hline \end{array} \][/tex]

Therefore, the value that should be subtracted from both sides is [tex]\(\boxed{1}\)[/tex].