How do you graph #abs(10x+8 ) >2 #?

Separate solving into 2 cases:

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To graph the absolute value inequality |10x + 8| > 2, first, we need to find the critical points where the expression inside the absolute value function equals 2 and -2.

1. Solve the equation 10x + 8 = 2: 10x = -6, x = -0.6.

2. Solve the equation 10x + 8 = -2: 10x = -10, x = -1.

These critical points divide the number line into three intervals: (-∞, -1), (-1, -0.6), and (-0.6, ∞).

Test a point from each interval in the original inequality to determine which intervals satisfy the inequality.

• Test x = -2: |10(-2) + 8| > 2, |10(-2) + 8| = |-20 + 8| = |-12| = 12, 12 > 2, true.

• Test x = -0.8: |10(-0.8) + 8| > 2, |10(-0.8) + 8| = |-8 + 8| = |0| = 0, 0 > 2, false.

• Test x = 0: |10(0) + 8| > 2, |10(0) + 8| = |8| = 8, 8 > 2, true.

Therefore, the solution to the inequality is (-∞, -1) ∪ (-0.6, ∞).

To graph this on a number line, draw an open circle at -1 and -0.6 to indicate that they are not included in the solution, and shade the intervals (-∞, -1) and (-0.6, ∞).

To graph the inequality ( \lvert 10x + 8 \rvert > 2 ), you can follow these steps:

1. Split the absolute value inequality into two separate inequalities:

   • ( 10x + 8 > 2 )
   • ( 10x + 8 < -2 )

2. Solve each inequality separately for ( x ):

For ( 10x + 8 > 2 ): [ 10x + 8 > 2 ] [ 10x > -6 ] [ x > -\frac{6}{10} ] [ x > -\frac{3}{5} ]

For ( 10x + 8 < -2 ): [ 10x + 8 < -2 ] [ 10x < -10 ] [ x < -1 ]

So, the solution to ( \lvert 10x + 8 \rvert > 2 ) is ( x > -\frac{3}{5} ) or ( x < -1 ).

Now, graph these two inequalities on a number line and shade the regions that satisfy each inequality:

• For ( x > -\frac{3}{5} ), shade the region to the right of ( -\frac{3}{5} ).
• For ( x < -1 ), shade the region to the left of ( -1 ).

The shaded regions together represent the solution to the inequality ( \lvert 10x + 8 \rvert > 2 ) on the number line.