On the SAT, you may be asked to solve a system of inequalities. For example, you may be asked to solve for x that satisfy both inequalities.
Solve for x in the following inequalities:
\[ 7x \ge 21 \]
\[ 2x \lt 10 \]
In order to find the values of x that would satisfy both inequalities, you have to solve each inequality, find out if there is any overlap, and create a range of possible values. So, first solve each inequality individually:
\[ \frac {7x}{7} \ge \frac{21}{7} \]
\[ x \ge 3 \]
and the second inequality:
\[ \frac {2x}{2} \lt \frac{10}{2}\]
\[ x \lt 5 \]
In order for a value of x to satisfy both inequalities, x must be greater than or equal to 3, but also less than 5. Therefore, you write a range of values that represents the possible solutions to both inequalities. You write:
\[ 3 \le x \lt 5 \]
You can check your answer by plugging in a value of from your solution set into both equations. Let's try 4:
\[ 7(4) \ge 21 \]
\[ 28 \ge 21 \]
and:
\[ 2(4) \lt 10 \]
\[ 8 \lt 10 \]
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