Math worksheet on solving equations using addition and subtraction, with examples and exercises.

Since the user has set all options (ExplainAnswer, TeachTopic, GeneratePractice) to false, I will provide the solutions to the problems presented in the image, following the required structure.

The image contains three sections of problems:
1. Solve each equation. Then check your solution. (Problems 1-12)
2. Write an equation for each problem. Then solve the equation and check the solution. (Problems 13-17)
3. A number divided by fourteen is equal to eighteen. What is the number? (Problem 18)

I will solve each problem step-by-step.

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Section 1: Solve each equation. Then check your solution.

1. $k + 1 = 9$
* Solve: Subtract 1 from both sides.
$k = 9 - 1$
$k = 8$
* Check: Substitute $k=8$ back into the original equation.
$8 + 1 = 9$ (Correct)

2. $x - 9 = 17$
* Solve: Add 9 to both sides.
$x = 17 + 9$
$x = 26$
* Check: Substitute $x=26$ back into the original equation.
$26 - 9 = 17$ (Correct)

3. $-3y - 5 = 16$
* Solve: Add 5 to both sides.
$-3y = 16 + 5$
$-3y = 21$
Divide by -3.
$y = 21 / -3$
$y = -7$
* Check: Substitute $y=-7$ back into the original equation.
$-3(-7) - 5 = 21 - 5 = 16$ (Correct)

4. $2y - 7 = 8$
* Solve: Add 7 to both sides.
$2y = 8 + 7$
$2y = 15$
Divide by 2.
$y = 15 / 2$ or $7.5$
* Check: Substitute $y=7.5$ back into the original equation.
$2(7.5) - 7 = 15 - 7 = 8$ (Correct)

5. $5.1x + 0.7 = 2.3$
* Solve: Subtract 0.7 from both sides.
$5.1x = 2.3 - 0.7$
$5.1x = 1.6$
Divide by 5.1.
$x = 1.6 / 5.1$
$x = 16 / 51$
* Check: Substitute $x = 16/51$ back into the original equation.
$5.1(16/51) + 0.7 = (51/10)(16/51) + 0.7 = 16/10 + 0.7 = 1.6 + 0.7 = 2.3$ (Correct)

6. $4.5 - \frac{1}{2}x = \frac{5}{2}$
* Solve: Convert decimals to fractions for easier calculation ($4.5 = 9/2$).
$\frac{9}{2} - \frac{1}{2}x = \frac{5}{2}$
Subtract $\frac{9}{2}$ from both sides.
$-\frac{1}{2}x = \frac{5}{2} - \frac{9}{2}$
$-\frac{1}{2}x = -\frac{4}{2}$
$-\frac{1}{2}x = -2$
Multiply by -2.
$x = 4$
* Check: Substitute $x=4$ back into the original equation.
$4.5 - \frac{1}{2}(4) = 4.5 - 2 = 2.5$
$\frac{5}{2} = 2.5$ (Correct)

7. $t - 15 = -17$
* Solve: Add 15 to both sides.
$t = -17 + 15$
$t = -2$
* Check: Substitute $t=-2$ back into the original equation.
$-2 - 15 = -17$ (Correct)

8. $-12 = -6t + 9$
* Solve: Subtract 9 from both sides.
$-12 - 9 = -6t$
$-21 = -6t$
Divide by -6.
$t = -21 / -6$
$t = 21 / 6$
$t = 7 / 2$ or $3.5$
* Check: Substitute $t=3.5$ back into the original equation.
$-12 = -6(3.5) + 9$
$-12 = -21 + 9$
$-12 = -12$ (Correct)

9. $8.7 - 0.2 = 1.5$
* Analysis: This appears to be a typo in the book. $8.7 - 0.2 = 8.5$, which does not equal $1.5$. There is no variable to solve for. Assuming it meant $8.7x - 0.2 = 1.5$ or similar, but without a clear variable, it's unsolvable as written. Let's assume it's $8.7 - 0.2x = 1.5$.
* Solve (assuming $8.7 - 0.2x = 1.5$):
Subtract 8.7 from both sides.
$-0.2x = 1.5 - 8.7$
$-0.2x = -7.2$
Divide by -0.2.
$x = -7.2 / -0.2$
$x = 72 / 2$
$x = 36$
* Check: $8.7 - 0.2(36) = 8.7 - 7.2 = 1.5$ (Correct)

10. $40 - 40 = -10$
* Analysis: Similar to #9, this is a false statement ($0 = -10$) with no variable. It is likely a typo. Perhaps it was meant to be $40 - 4x = -10$ or $40 - 40x = -10$. Without clarification, it cannot be solved. Let's try $40 - 4x = -10$.
* Solve (assuming $40 - 4x = -10$):
Subtract 40 from both sides.
$-4x = -10 - 40$
$-4x = -50$
Divide by -4.
$x = -50 / -4$
$x = 12.5$
* Check: $40 - 4(12.5) = 40 - 50 = -10$ (Correct)

11. $11m - (-12) = 10$
* Solve: Simplify the double negative.
$11m + 12 = 10$
Subtract 12 from both sides.
$11m = 10 - 12$
$11m = -2$
Divide by 11.
$m = -2 / 11$
* Check: Substitute $m = -2/11$ back into the original equation.
$11(-2/11) - (-12) = -2 + 12 = 10$ (Correct)

12. $\frac{1}{4}x - \frac{1}{2} = 1$
* Solve: Add $\frac{1}{2}$ to both sides.
$\frac{1}{4}x = 1 + \frac{1}{2}$
$\frac{1}{4}x = \frac{3}{2}$
Multiply by 4.
$x = \frac{3}{2} * 4$
$x = \frac{12}{2}$
$x = 6$
* Check: Substitute $x=6$ back into the original equation.
$\frac{1}{4}(6) - \frac{1}{2} = \frac{6}{4} - \frac{1}{2} = \frac{3}{2} - \frac{1}{2} = \frac{2}{2} = 1$ (Correct)

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Section 2: Write an equation for each problem. Then solve the equation and check the solution.

13. Twelve subtracted from a number equals 23. Find the number.
* Equation: Let the number be $n$.
$n - 12 = 23$
* Solve: Add 12 to both sides.
$n = 23 + 12$
$n = 35$
* Check: $35 - 12 = 23$ (Correct)

14. What number decreased by 32 equals -15?
* Equation: Let the number be $n$.
$n - 32 = -15$
* Solve: Add 32 to both sides.
$n = -15 + 32$
$n = 17$
* Check: $17 - 32 = -15$ (Correct)

15. Fifty subtracted from a number equals eighty. Find the number.
* Equation: Let the number be $n$.
$n - 50 = 80$
* Solve: Add 50 to both sides.
$n = 80 + 50$
$n = 130$
* Check: $130 - 50 = 80$ (Correct)

16. What number minus one-half is equal to negative one-half?
* Equation: Let the number be $n$.
$n - \frac{1}{2} = -\frac{1}{2}$
* Solve: Add $\frac{1}{2}$ to both sides.
$n = -\frac{1}{2} + \frac{1}{2}$
$n = 0$
* Check: $0 - \frac{1}{2} = -\frac{1}{2}$ (Correct)

17. The difference of a number and eight is equal to 14. What is the number?
* Equation: Let the number be $n$. "Difference of a number and eight" usually means $n - 8$.
$n - 8 = 14$
* Solve: Add 8 to both sides.
$n = 14 + 8$
$n = 22$
* Check: $22 - 8 = 14$ (Correct)

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Section 3: Word Problem

18. A number divided by fourteen is equal to eighteen. What is the number?
* Equation: Let the number be $n$.
$\frac{n}{14} = 18$
* Solve: Multiply both sides by 14.
$n = 18 * 14$
$n = 252$
* Check: $252 / 14 = 18$ (Correct)

Final Answer:
1. k = 8
2. x = 26
3. y = -7
4. y = 7.5
5. x = 16/51
6. x = 4
7. t = -2
8. t = 3.5
9. Assuming typo, if 8.7 - 0.2x = 1.5, then x = 36
10. Assuming typo, if 40 - 4x = -10, then x = 12.5
11. m = -2/11
12. x = 6
13. n = 35
14. n = 17
15. n = 130
16. n = 0
17. n = 22
18. n = 252