How do you solve and graph #x-3>7#?

1 Answer
May 28, 2017

Express the inequality as an equation, then test points to determine where to shade the graph.

Explanation:

Strategy: Express the inequality as an equation (i.e., with an equals sign). Graph the equation. Strict inequality lines are drawn as a dashed line. Shade the side of the line where the inequality is true.

Step 1. Express the inequality as an equation.

#x-3=7#
#x=10#

Step 2. Graph the equation. Because #># is a strict inequality, the line should be drawn as dashed.

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Step 3. Shade the side of the line where the inequality is true.

Trying #(0,0)# makes the given inequality #x-3>7# FALSE.

#x-3>7#
#0-3>7#
#-3>7# is FALSE, because #-3# is not greater than #7#

So don't shade that side of the line. However, trying the point #(12,0)# makes the given inequality TRUE.

#x-3>7#
#12-3>7#
#9>7# is TRUE, because #9# is indeed greater than #7#. So go ahead and shade the right side of the line.

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