How do you graph the system of linear inequalities #y>2x7# and #4x+4y<12#?
Plot the two lines. The solution is the set of points between them. The lines should be dotted (not included in the solution) and the space between the lines shaded.
Arrange the equations into standard format (y < ax + b). Calculate and plot some points. Check for the solution range for each inequality. Locate the common solution space for both inequalities.
By signing up, you agree to our Terms of Service and Privacy Policy
To graph the system of linear inequalities (y > 2x  7) and (4x + 4y < 12):

Graph the boundary lines for each inequality:
 For (y > 2x  7), graph the line (y = 2x  7), but use a dashed line because it's a strict inequality (does not include the line itself).
 For (4x + 4y < 12), graph the line (4x + 4y = 12), but again use a dashed line because it's a strict inequality.

Choose a test point not on the boundary lines and plug it into each inequality to determine which region to shade:
 For example, the origin (0,0) is a common test point.
 For (y > 2x  7), if (0,0) satisfies the inequality, shade the region above the line; if not, shade the region below the line.
 For (4x + 4y < 12), if (0,0) satisfies the inequality, shade the region on the same side as the origin; if not, shade the region on the opposite side.

The intersection of the shaded regions represents the solution set for the system of inequalities.
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
 How do you write the interval [5, +infinity) as an inequality involving x and show each inequality using the real number line?
 Keith has $500 in a savings account at the beginning of the summer. He wants to have at least $200 at the end of the summer. He withdraws $25 per week for food, clothing, and movie tickets. How many weeks can Keith withdraw money from his account?
 How do you solve the system #x = y + 4# and #2x  5y = 2# by substitution?
 A drawer contains exactly 5 red, 4 blue and 3 green pencils. if two of the pencils are selected at random one after the other without replacing the first, what is the probability that the first one is red and the second one is green?
 How do you solve #6+ 8x < 2(  3+ 4x )#?
 98% accuracy study help
 Covers math, physics, chemistry, biology, and more
 Stepbystep, indepth guides
 Readily available 24/7