Continuing to Payment will take you to apayment page

Purchasing
SparkNotes PLUS
for a group?

Get Annual Plans at a discount when you buy 2 or more!

Price

$24.99$18.74/subscription + tax

Subtotal $37.48 + tax

Save 25%
on 2-49 accounts

Save 30%
on 50-99 accounts

Want 100 or more?
Contact us
for a customized plan.

Continuing to Payment will take you to apayment page

Your Plan

Payment Details

Payment Details

Payment Summary

SparkNotes Plus

You'll be billed after your free trial ends.

7-Day Free Trial

Not Applicable

Renews February 29, 2024February 22, 2024

Discounts (applied to next billing)

DUE NOW

US $0.00

SNPLUSROCKS20 | 20%Discount

This is not a valid promo code.

Discount Code(one code per order)

SparkNotes PLUS
Annual Plan - Group Discount

Qty: 00

SubtotalUS $0,000.00

Discount (00% off)
-US $000.00

TaxUS $XX.XX

DUE NOWUS $1,049.58

SparkNotes Plus subscription is $4.99/month or $24.99/year as selected above. The free trial period is the first 7 days of your subscription. TO CANCEL YOUR SUBSCRIPTION AND AVOID BEING CHARGED, YOU MUST CANCEL BEFORE THE END OF THE FREE TRIAL PERIOD. You may cancel your subscription on your Subscription and Billing page or contact Customer Support at custserv@bn.com. Your subscription will continue automatically once the free trial period is over. Free trial is available to new customers only.

Choose Your Plan

Your Free Trial Starts Now!

For the next 7 days, you'll have access to awesome PLUS stuff like AP English test prep, No Fear Shakespeare translations and audio, a note-taking tool, personalized dashboard, & much more!

Thank You!

You’ve successfully purchased a group discount. Your group members can use the joining link below to redeem their group membership. You'll also receive an email with the link.

No URL

Copy

Members will be prompted to log in or create an account to redeem their group membership.

Thanks for creating a SparkNotes account! Continue to start your free trial.

Please wait while we process your payment

Your PLUS subscription has expired

We’d love to have you back! Renew your subscription to regain access to all of our exclusive, ad-free study tools.

Recall that a number line is a
horizontal line that has points which correspond to numbers. The
points are spaced according to the value of the number they correspond
to; in a number line containing only whole numbers or integers, the
points are equally spaced.

We can graph real numbers by representing them as points on the number
line. For example, we can graph "2" on the number
line:

We can also graph inequalities on the number line. The following graph
represents the inequality x≤2. The dark line
represents all the numbers that satisfy x≤2. If we
pick any number on the dark line and plug it in for x, the inequality
will be true.

The following graph represents the inequality x < 2. Note
that the open circle on 2 shows that 2 is not a
solution to x < 2.

Here are the graphs of x > 2 and x≥2,
respectively:

An inequality with a "≠" sign has a solution set which is all the
real numbers except a single point (or a number of single points).
Thus, to graph an inequality with a "≠" sign, graph the entire
line with one point removed. For example, the graph of x≠2 looks like:

Using the Number Line to Solve Inequalities

We can use the number line to solve inequalities containing <, ≤,
>, and ≥. To solve an inequality using the number line, change
the inequality sign to an equal sign, and solve the equation. Then
graph the point on the number line (graph it as an open circle if the
original inequality was "<" or ">"). The number line should now be
divided into 2 regions -- one to the left of the point and one to the
right of the point

Next, pick a point in each region and "test" it -- see if it satisfies
the inequality when plugged in for the variable. If it satisfies the
inequality, draw a dark line from the point into that region, with an
arrow at the end. This is the solution set to the equation: if one point in the region satisfies the inequality, the entire region will satisfy the inequality.

Example: -3(x - 2)≤12

Solve -3(x - 2) = 12:

x - 2 = - 4 x = - 2

Graph x = - 2, using a filled circle because the original
inequality was ≤:
Plug values into the equation -3(x - 2)≤12:

Pick a point on the left of -2 (-3, for example): -3(- 3 - 2)≤12 ? 15≤12 ? No.
Pick a point on the right of -2 (0, for example): -3(0 - 2)≤12 ? 6≤12 ? Yes.

Draw a dark line from -2 extending to the right, with an arrow at the
end: