1. **State the problem:** We need to match each inequality with the correct graph letter based on the description of the solution set. 2. **Recall inequality graph rules:** - $x < a$: open circle at $a$, shading to the left. - $x \leq a$: closed circle at $a$, shading to the left. - $x > a$: open circle at $a$, shading to the right. - $x \geq a$: closed circle at $a$, shading to the right. - $x \neq a$: all real numbers except $a$ (usually entire line with a hole at $a$). - Entire real line: shading both directions. 3. **Match each inequality to graph letter:** (1) $x < 2$ matches graph O (open circle at 2, shading left). (2) $x \leq 2$ matches graph X (closed circle at 2, shading left). (3) $x > 2$ matches graph C (shading right from 2). (4) $x \geq 2$ matches graph C (closed circle at 2, shading right) but only C is described as shading right, so C. (5) $x \neq 1$ matches graph I (open circle at 1, arrows both directions). (6) $x < -1$ matches graph S (open circle at -1, shading left). (7) $x > -1$ matches graph M (open circle at 1, shading right) but for -1, shading right with open circle is M or B? B is shading right, no circle mentioned, M is open circle at 1 shading right, so for $x > -1$ best match is B (shading right). (8) $x \leq -1$ matches graph W (closed circle at -1, shading left). (9) $x \geq -1$ matches graph B (shading right) or U (filled circle at 1 with double arrow) but for -1, shading right with closed circle is not given, so B. (10) $x < 1$ matches graph O or I? I is open circle at 1 with arrows both directions, O is open circle at 2 shading left, so I. (11) $1 < x$ matches graph M (open circle at 1, shading right). (12) $-3 \leq x$ matches graph E or G or N (entire line shaded both directions). Since $-3 \leq x$ means shading from -3 rightwards, but no graph explicitly shows that, closest is C or B (shading right). So B. (13) $x > -3$ matches graph B (shading right). (14) $x \neq -1$ matches graph I or A? I is open circle at 1, so no. A is empty line, no circles. No exact match, but graph I is closest for $x \neq 1$, so for $x \neq -1$ likely I. (15) $0 \geq x$ means $x \leq 0$, shading left with closed circle at 0, no graph with circle at 0, so closest is R or D (shading left). Choose R. (16) $0 \leq x$ means shading right from 0, no circle at 0, so B. (17) $0 > x$ means $x < 0$, shading left open circle at 0, no circle at 0 graph, so D or R, choose D. (18) $0 < x$ means shading right open circle at 0, no circle at 0 graph, so M or B, choose B. 4. **Final answers:** (1) O (2) X (3) C (4) C (5) I (6) S (7) B (8) W (9) B (10) I (11) M (12) B (13) B (14) I (15) R (16) B (17) D (18) B This matches each inequality to the graph letter based on the descriptions and standard graphing rules for inequalities.