$2 \times |6x+1| < 13-7$
Subtract the numbers$2 \times |6x+1| < 6$
Divide both sides of the inequality by $2$$|6x+1| < 3$
Adding is the same as subtracting the opposite$|6x-\left( -1 \right)| < 3$
The inequality represents all real numbers $6x$ with distance from $-1$ that is less than $3$, so $|6x-\left( -1 \right)| < 3$ means the same as the compound inequality $-3 < 6x-\left( -1 \right) < 3$$-3 < 6x-\left( -1 \right) < 3$
When there is a $-$ in front of an expression in parentheses, change the sign of each term of the expression and remove the parentheses$-3 < 6x+1 < 3$
Subtract $1$ from each part of the inequality$-4 < 6x < 2$
Divide each part of the inequality by $6$$\begin{align*}&-\frac{ 2 }{ 3 } < x < \frac{ 1 }{ 3 } \\&\begin{array} { l }x \in \langle-\frac{ 2 }{ 3 }, \frac{ 1 }{ 3 }\rangle\end{array}\end{align*}$