Inequalities (multi-step)

Advanced Math 7 · Unit 11 · linear-inequalities-7 · Teacher edition

linear-inequalities-7

Name ______________________________Date ______________

1.
Solve $3x + 5 < 20$ . Enter the largest integer that satisfies it.
Answer: ______________
2.
Solve $5 - 2x > 11$ . Enter the largest integer that satisfies it.
Answer: ______________
3.
On a number line, a closed circle is drawn at $-1$ , an open circle at $4$ , and the segment between them is shaded. Which inequality is graphed?
1. (A)
  $-1 < x < 4$
2. (B)
  $-1 \le x < 4$
3. (C)
  $-1 < x \le 4$
4. (D)
  $-1 \le x \le 4$
4.
Solve $-2x + 7 > 13$ .
1. (A)
  $x < 3$
2. (B)
  $x > -3$
3. (C)
  $x > 3$
4. (D)
  $x < -3$
5.
How many integers $x$ satisfy $1 \le 7 - 2x < 15$ ?
Answer: ______________

Answer key — Inequalities (multi-step)

1.
4linear-inequalities-7-01
$3x < 15 \Rightarrow x < 5$ . The largest integer less than $5$ is $\mathbf{4}$ ( $5$ gives $20 < 20$ , which is false).
2.
-4linear-inequalities-7-02
$5 - 2x > 11 \Rightarrow -2x > 6 \Rightarrow x < -3$ . The largest integer less than $-3$ is $\mathbf{-4}$ . Check: $5 - 2(-4) = 13 > 11$ ✓, while $x = -3$ gives $11 > 11$ , false.
3.
(B)
$-1 \le x < 4$
linear-inequalities-7-03
$-1$ is included and $4$ is not: $\mathbf{-1 \le x < 4}$ .
4.
(D)
$x < -3$
linear-inequalities-7-04
$-2x > 6 \Rightarrow x < -3$ : $\mathbf{x < -3}$ . Check $x = -10$ : $20 + 7 = 27 > 13$ ✓. ( $x > -3$ forgets to reverse; test $x = 0$ : $7 > 13$ is false.)
5.
7linear-inequalities-7-05
$-6 \le -2x < 8 \Rightarrow 3 \ge x > -4$ , so $x \in \{-3, -2, -1, 0, 1, 2, 3\}$ : $\mathbf{7}$ integers. Check the ends: $x = 3$ gives $7 - 6 = 1$ ✓; $x = -4$ gives $15$ , which is not $< 15$ .