MATH SOLVE

4 months ago

Q:
# choose the correct description of the graph of the compound inequality: 3x + 1 > 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[tex]3x+1 > 7[/tex]-------> inequality A[tex]4x\leq 24[/tex] -------> inequality BStep 1Solve inequality A[tex]3x+1 > 7\\ \\3x > 7-1 \\ \\x> 2[/tex]the solution is the interval------> (2,β)Step 2Solve inequality B[tex]4x\leq 24\\ \\x\leq 6[/tex]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