To set of values obtained in exercise 142 and 143 using the table feature of a graphing utility. Given: From Exercise 142, the inequality is −3(x−6)&gt;2x−2. From Exercise 143, the expression is −2(x+4)&gt;6x+16.

Question

To set of values obtained in exercise 142 and 143 using the table feature of a graphing utility.  Given: From Exercise 142, the inequality is −3(x−6)&amp;gt;2x−2.  From Exercise 143, the expression is −2(x+4)&amp;gt;6x+16.

Paul Mitchell · Accepted Answer

Proof:&amp;nbsp;Consider the inequality&amp;nbsp;−3(x−6)&amp;gt;2x−2&amp;nbsp;To find the inequality&#039;s solutions, take the following actions:Step 1: Open the TI83 calculator. Plot the equations on the left and right by clicking the &quot;Y=&quot; button.Step 2: Use Table feature of TI83 calculator. First press &quot;2nd&quot; and then &quot;Graph&quot; button to get the table of both the inequalities.&amp;nbsp;XY1Y2018−2115021223944665386010&amp;nbsp;Step 3: The values of equations&amp;nbsp;−3(x−6)&amp;nbsp;&amp;nbsp;and&amp;nbsp;&amp;nbsp;2x−2&amp;nbsp;are equal at&amp;nbsp;x=4.At&amp;nbsp;x=4, value of both the equations is 6.&amp;nbsp;So, for&amp;nbsp;x&amp;lt;4, the graph of left-hand side equation lies above the graph of right-hand side equation.&amp;nbsp;Consider the inequality&amp;nbsp;−2(x+4)&amp;gt;6x+16&amp;nbsp;Use the following steps to obtain the solutions of the inequality&amp;nbsp;Step 1: Open the TI83 calculator. Go to &quot;Y=&quot; button and plot the left-hand and right-hand equations.&amp;nbsp;Step 2: Use table feature of TI83 calculator. First press &quot;2nd&quot; and then &quot;Graph&quot; button to get the table of both the equations as follows:&amp;nbsp;XY1Y2−64−20−52−14−40−8−3−2−2−2−44−1−6100−816&amp;nbsp;Step 3: The values of equations&amp;nbsp;−2(x+4)&amp;nbsp;&amp;nbsp;and&amp;nbsp;&amp;nbsp;6x+16&amp;nbsp;are equal at&amp;nbsp;x=−3. At&amp;nbsp;x=−3, value of both the equations is -2.&amp;nbsp;So, for&amp;nbsp;x&amp;lt;−3, the graph of left-hand side equation lies above to graph of right-hand side equuation.&amp;nbsp;Hence, the results are verified.

ol3i4c5s4hr · Accepted Answer

Step 1  Given:  From Exercise 142, the inequality is −3(x−6)&amp;gt;2x−2  From Exercise 142, the expression is −2(x+4)&amp;gt;6x+16  The table  XY1Y2018−2115021223944665386010  Step 2  consider the inequality −2(x+4)&amp;gt;6x+16  The table:  XY1Y2−64−20−52−14−40−8−3−2−2−2−44−1−6100−816  So, fro x&amp;lt;−3, the graph of left-hand side equation lies above to graph of right-hand side equation.

To set of values obtained in exercise 142 and 143

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