How do you graph the inequality #x + 5 >2x + 1# and #-4x < -8#?

From the first, x < 4.

The combined inequality is 2 < x < 4 and the graph for this is the

segment of the x-axis, in between x = 2 and x = 4.

To graph the inequality ( x + 5 > 2x + 1 ), you would first isolate ( x ) on one side of the inequality sign. Then, you would graph the line representing the equation ( x + 5 = 2x + 1 ), but you would use a dashed line because the inequality is strictly greater than. Finally, you would shade the region above the line, indicating all the values of ( x ) that satisfy the inequality.

To graph the inequality ( -4x < -8 ), you would first isolate ( x ) by dividing both sides of the inequality by -4. Then, you would graph the line representing the equation ( -4x = -8 ), but you would again use a dashed line because the inequality is strictly less than. Finally, you would shade the region below the line, indicating all the values of ( x ) that satisfy the inequality.