Q:

# choose the correct description of the graph of the compound inequality: 3x + 1 &gt; 7 and 4x less than or equal to 24A. a number line with an open circle on 2, a closed circle on 6, and shading in between. B. a number line with an open circle on 2, shading to the left, and a closed circle on 6, and shading to the right.C. a number line with a closed circle on 2, shading to the left, and open circle on 6, and shading to the right.D. a number line with a closed circle on 2, an open circle on 6, and shading in between.

Accepted Solution

A:
we have$$3x+1 > 7$$-------> inequality A$$4x\leq 24$$ -------> inequality BStep 1Solve inequality A$$3x+1 > 7\\ \\3x > 7-1 \\ \\x> 2$$the solution is the interval------> (2,β)Step 2Solve inequality B$$4x\leq 24\\ \\x\leq 6$$the solution is the interval------> (-β,6]Step 3Find the solution of the compound inequalitySolution A β© Solution B(2,β) β© (-β,6]=(2,6]thereforethe answer is the option Aa number line with an open circle on 2, a closed circle on 6, and shading in between