20 medium SAT Linear inequalities questions

A caterer is preparing gift baskets containing cookies and brownies. Each basket with cookies weighs 2 pounds, and each basket with brownies weighs 3 pounds. The caterer's delivery vehicle can carry at most 180 pounds. The caterer must prepare at least 25 baskets with cookies to fulfill orders. What is the maximum number of baskets with brownies the caterer can prepare for this delivery?

• A$60$
• B$43$
• C$45$
• D$50$

A number y is at most 10 less than 4 times the value of z. If z is 11, what is the greatest possible value of y?

• A$1$
• B$34$
• C$44$
• D$54$

In the xy-plane, a line with slope $\displaystyle \frac{1}{2}$ passes through the point (4, 3). The region below the line, including the line itself, is shaded. Which inequality represents the graph?

• A$\displaystyle y \le (\frac{1}{2})x + 5$
• B$\displaystyle y < (\frac{1}{2})x + 1$
• C$x \le 2y - 2$
• D$\displaystyle y \le (\frac{1}{2})x + 1$

Which inequality is equivalent to $15 - 5(x + 1) \le 0$?

• A$x \le 2$
• B$x \ge 2$
• C$x \le 3$
• D$x \ge 3$

Which inequality is equivalent to $7x - 12 \le 3(x + 4)$?

• A$x \ge 6$
• B$x \le 0$
• C$x \ge -6$
• D$x \le 6$

A factory produces chairs and tables. Each chair requires 3 hours of labor and each table requires 5 hours of labor. The factory has at most 240 hours of labor available per week. Additionally, the factory must produce at least 20 chairs per week to meet customer demand. What is the maximum number of tables the factory can produce in one week?

• A$48$
• B$40$
• C$36$
• D$60$

A number h is at most 11 less than 6 times the value of j. If j is 10, what is the greatest possible value of h?

• A$60$
• B$49$
• C$71$
• D$5$

In the xy-plane, a line has x-intercept 4 and y-intercept -6. The region below the line, not including the line itself, is shaded. Which inequality represents the graph?

• A$\displaystyle y < (\frac{3}{2})x - 6$
• B$\displaystyle y \le (\frac{3}{2})x - 6$
• C$\displaystyle y < (-\frac{3}{2})x - 6$
• D$\displaystyle x < (\frac{2}{3})y + 4$

Which inequality is equivalent to $6(x + 2) - 4x \le 36$?

• A$x \le 6$
• B$x \ge 12$
• C$x \ge 6$
• D$x \le 12$

Which inequality is equivalent to $15 - 3x \ge 6x + 24$?

• A$x \ge -1$
• B$x \le -13$
• C$x \ge 13$
• D$x \le -1$

A community center offers yoga classes and dance classes. Each yoga class can accommodate 8 participants, and each dance class can accommodate 12 participants. The center has space for at most 192 total participants across all classes in a session. The center must offer at least 6 yoga classes to meet member preferences. What is the maximum number of dance classes the center can offer in one session?

• A$16$
• B$14$
• C$12$
• D$24$

A number w is at most 9 less than 2 times the value of t. If t is 15, what is the greatest possible value of w?

• A$21$
• B$39$
• C$6$
• D$30$

In the xy-plane, a line passes through the origin and the point (3, 2). The region above the line, including the line itself, is shaded. Which inequality represents the graph?

• A$\displaystyle y \ge (\frac{3}{2})x$
• B$\displaystyle y \ge (\frac{2}{3})x$
• C$\displaystyle y > (\frac{2}{3})x$
• D$\displaystyle y \le (\frac{2}{3})x$

Which inequality is equivalent to $3(x - 5) + 2x \ge 20$?

• A$x \ge 5$
• B$x \le 7$
• C$x \ge 7$
• D$x \le 5$

Which inequality is equivalent to -$2(x - 8) < 20$?

• A$x < -2$
• B$x > 18$
• C$x > -2$
• D$x < 18$

A warehouse stores small boxes and large boxes. Each small box occupies 6 cubic feet of space, and each large box occupies 10 cubic feet of space. The warehouse has at most 480 cubic feet of available storage space. The warehouse must store at least 15 small boxes for inventory requirements. What is the maximum number of large boxes the warehouse can store?

• A$39$
• B$48$
• C$40$
• D$80$

A number a is at most 8 less than 3 times the value of b. If b is 14, what is the greatest possible value of a?

• A$42$
• B$6$
• C$34$
• D$50$

In the xy-plane, a line passes through the origin and has $\displaystyle slope -\frac{3}{4}$. The region above the line, not including the line itself, is shaded. Which inequality represents the graph?

• A$\displaystyle y > (-\frac{4}{3})x$
• B$\displaystyle y < (-\frac{3}{4})x$
• C$\displaystyle y \ge (-\frac{3}{4})x$
• D$\displaystyle y > (-\frac{3}{4})x$

Which inequality is equivalent to $7 - 3x \le 2(x - 4)$?

• A$x \le 3$
• B$x \ge 3$
• C$x \ge -1$
• D$x \le -1$

Which inequality is equivalent $to -6(x - 3) \ge 42$?

• A$x \ge -4$
• B$x \le -10$
• C$x \le -4$
• D$x \ge 10$