Question: User: 1. 8x − 6 ≥ 10
2. 23 − 4u < 11
3. −16 − 8r ≥ 0
4. 14c < 9c + 5
5. 9x − 11 > 6x − 9
6. −3(4w − 1) > 18
7. 1 − 8u ≤ 3u − 10
8. 17.5 < 19 − 2.5x
9. 9(2r − 5) − 3 < 7r − 4
10. 1 + 5(x − 8) ≤ 2 − (x + 5)
11. (4x − 3)/2 ≥ −3.5
12. q − 2(2 − q) ≤ 0
13. −36 − 2(w + 77) > −4(2w + 52)
14. 4n − 5(n − 3) > 3(n + 1) − 4
1: graph is a number line centered around integers −4 to 4, with solution x ≥ 2; closed dot at 2 and shading to the right. position_hint: center
2: graph is a number line centered around integers −2 to 6, with solution u > 3; open dot at 3 and shading to the right. position_hint: center
3: graph is a number line centered around integers −4 to 4, with solution r ≤ −2; closed dot at −2 and shading to the left. position_hint: center
4: graph is a number line centered around integers −4 to 4, with solution c < 1; open dot at 1 and shading to the left. position_hint: center
5: graph is a number line centered around integers −4 to 4, with solution x > 2/3; open dot between 0 and 1, shading to the right. position_hint: center
6: graph is a number line centered around integers −4 to 4, with solution w < −3/2; open dot halfway between −2 and −1, shading to the left. position_hint: center
7: graph is a number line centered around integers −4 to 4, with solution u ≥ 1; closed dot at 1 and shading to the right. position_hint: center
8: graph is a number line centered around integers −4 to 4, with solution x > −1/2; open dot halfway between −1 and 0, shading to the right. position_hint: center
9: graph is a number line centered around integers −2 to 6, with solution r < 11/2; open dot halfway between 5 and 6, shading to the left. position_hint: center
10: graph is a number line centered around integers 0 to 8, with solution x ≥ 4; closed dot at 4 and shading to the right. position_hint: center
11: graph is a number line centered around integers −4 to 4, with solution x ≥ −1/2; closed dot halfway between −1 and 0, shading to the right. position_hint: center
12: graph is a number line centered around integers −4 to 4, with solution q ≤ 1; closed dot at 1 and shading to the left. position_hint: center
13: graph is a number line centered around integers −4 to 4, with solution w > −35/2; open dot halfway between −18 and −17, shading to the right. position_hint: center
14: graph is a number line centered around integers −2 to 6, with solution n < 8; open dot at 8 and shading to the left. position_hint: center
15. Let x be the number.
x − 20 > 2x
x < −20
16. Let x be the number.
4(2x − 3) < 5.5x
x < 12
17. Let x be the number of nights.
90x + 90(0.1)x + 12x + 30 ≤ 600
111x + 30 ≤ 600
111x ≤ 570
x ≤ 570/111
x ≤ 5.13...
The Lincoln’s can stay at most 5 nights.
18. Let x be the amount withdrawn.
3800 − x − 750 ≥ 500
3050 − x ≥ 500
−x ≥ −2550
x ≤ 2550
1. **State the problem:** Solve the inequality $$8x - 6 \geq 10$$.
2. **Use the inequality rules:** To isolate $$x$$, add 6 to both sides:
$$8x - 6 + 6 \geq 10 + 6$$
$$8x \geq 16$$
3. **Divide both sides by 8:**
$$\frac{\cancel{8}x}{\cancel{8}} \geq \frac{16}{8}$$
$$x \geq 2$$
4. **Interpretation:** The solution is all $$x$$ values greater than or equal to 2.
5. **Graph description:** On a number line centered from -4 to 4, place a closed dot at 2 and shade all values to the right.
**Final answer:** $$x \geq 2$$