Which graph represents the solution to 7xgt 21 or 6x-9lt 21 ? e -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 -8 -7 -6 -5 4 -3 -2 -1 0 1 2 3 4 5 6 7 8 4 t t t t t t -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 t t t t -8 -5 -5 -4 -3 -1 0 1 2 3 4 5 6 7 8

To solve the inequality $7x > 21$, we need to isolate the variable $x$ by dividing both sides of the inequality by 7:<br /><br />$7x > 21$<br />$x > 3$<br /><br />So the solution to the inequality $7x > 21$ is $x > 3$.<br /><br />To solve the inequality $6x - 9 < 21$, we need to isolate the variable $x$ by adding 9 to both sides of the inequality and then dividing by 6:<br /><br />$6x - 9 < 21$<br />$6x < 30$<br />$x < 5$<br /><br />So the solution to the inequality $6x - 9 < 21$ is $x < 5$.<br /><br />Now let's analyze the given graphs to determine which one represents the solution to the inequalities $7x > 21$ or $6x - 9 < 21$.<br /><br />The first graph shows a number line with values from -8 to 8. The second graph shows a number line with values from -8 to 8, but with some points marked as "t". The third graph shows a number line with values from -8 to 8, and the fourth graph shows a number line with values from -8 to 8, with some points marked as "t".<br /><br />The correct graph should represent the solution to the inequalities $7x > 21$ or $6x - 9 < 21$, which means it should show the values of $x$ that satisfy either of the inequalities.<br /><br />Looking at the graphs, we can see that the first graph does not represent the solution to the inequalities, as it does not show any points that satisfy either inequality.<br /><br />The second graph shows some points marked as "t", but it does not represent the solution to the inequalities either.<br /><br />The third graph shows a number line with values from -8 to 8, and it includes the point $x = 3$, which satisfies the inequality $7x > 21$. However, it does not include the point $x = 5$, which satisfies the inequality $6x - 9 < 21$.<br /><br />The fourth graph shows a number line with values from -8 to 8, and it includes the points $x = 3$ and $x = 5$, which satisfy both inequalities.<br /><br />Therefore, the correct graph that represents the solution to the inequalities $7x > 21$ or $6x - 9 < 21$ is the fourth graph.