# Calculate: 7+2 \times |6x+1| < 13

## Expression: $7+2 \times |6x+1| < 13$

Move the constant to the right-hand side and change its sign

$2 \times |6x+1| < 13-7$

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*}

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