Q63. - Algebra 2

Question

Solve each inequality.

$\left|y+1\right|<7$

Step-by-Step Solution

Answer

The required solution of the given inequality is $-8<y<6$ or $\left(-8,6\right)$.

Step 1 &ndash; Properties of inequality.

In an absolute inequality, if $\left|x\right|<a$, then $-a<x<a$.

According to the subtraction property of inequality, if $a<b$, then $a-c<b-c$, where $a,b,c$ are real values.

Step 2 &ndash; Given information.

The given inequality is:

$\left|y+1\right|<7$

Step 3 &ndash; Use the properties of inequality to solve the given inequality.

$\left|y+1\right|<7$

It is an absolute inequality and it can be written as:

$-7<y+1<7$

Subtract $1$ from each side of the above inequality.

$\begin{array}{l}-7-1<y+1-1<7-1\\ -8<y<6\end{array}$

The value of $y$ lies between $-8$ and $6$, where $-8$ and $6$ are excluded.

Thus, the required solution of the given inequality is $-8<y<6$ or $\left(-8,6\right)$.