Q57. - Algebra 1

Question

Solve and check the inequality $22>m-8$

Step-by-Step Solution

Answer

The solution is $30>m$

Step 1. Solving the inequality.

$\begin{array}{l}22>m-8\\ \Rightarrow 22+8>m-8+8\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}[\hspace{0.17em}Add\hspace{0.17em}\hspace{0.17em}to\hspace{0.17em}\hspace{0.17em}}8\text{\hspace{0.17em}\hspace{0.17em}both\hspace{0.17em}\hspace{0.17em}sides\hspace{0.17em}]\hspace{0.17em}}\\ \Rightarrow 30>m\end{array}$

Step 2. Example for finding total rent.

The solution $10>m+5$ is given by:

$\begin{array}{l}10>m+5\\ \Rightarrow m+5<10\\ \Rightarrow m+5-5<10-5\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}[Subtracting 5 from both sides]}\\ \Rightarrow m<5\end{array}$

Step 3. Checking the inequality.

$\begin{array}{l}\text{Check\hspace{0.17em}\hspace{0.17em}the\hspace{0.17em}\hspace{0.17em}solution\hspace{0.17em}\hspace{0.17em}when\hspace{0.17em}\hspace{0.17em}}m=25\\ 22>m-8\\ 22+8>m-8+8\\ 30>m\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}True\hspace{0.17em}\hspace{0.17em}statement.}\end{array}$

The solution of the inequality equation is $30>m$

Thus, the solution of the inequality equation $22>m-8$ is $30>m$