Pre-Algebra exam worksheet featuring equations to solve using basic operations, with examples and practice problems.

Here are the solutions to the problems on your worksheet. I have solved them step-by-step below.

Part 1: Solve by Adding or Subtracting

To solve these, you need to do the opposite operation to get the variable alone. If a number is being subtracted, add it. If a number is being added, subtract it.

(1) $h - 7 = 11$
* Add 7 to both sides: $11 + 7 = 18$
* $h = 18$

(2) $g + 15 = 25$
* Subtract 15 from both sides: $25 - 15 = 10$
* $g = 10$

(3) $w + 11 = 14$
* Subtract 11 from both sides: $14 - 11 = 3$
* $w = 3$

(4) $g + 14 = 23$
* Subtract 14 from both sides: $23 - 14 = 9$
* $g = 9$

(5) $i + 13 = 24$
* Subtract 13 from both sides: $24 - 13 = 11$
* $i = 11$

(6) $w - 4 = 5$
* Add 4 to both sides: $5 + 4 = 9$
* $w = 9$

(7) $27 = z + 14$
* Subtract 14 from both sides: $27 - 14 = 13$
* $z = 13$

(8) $8 = m - 4$
* Add 4 to both sides: $8 + 4 = 12$
* $m = 12$

(9) $x - 15 = 3$
* Add 15 to both sides: $3 + 15 = 18$
* $x = 18$

(10) $d - 15 = 10$
* Add 15 to both sides: $10 + 15 = 25$
* $d = 25$

(11) $k + 12 = 18$
* Subtract 12 from both sides: $18 - 12 = 6$
* $k = 6$

(12) $3 = s - 3$
* Add 3 to both sides: $3 + 3 = 6$
* $s = 6$

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Part 2: Solve by Multiplying or Dividing

To solve these, do the opposite of what is happening to the variable. If it's multiplied, divide. If it's divided, multiply.

(1) $5q = -15$
* Divide by 5: $-15 / 5 = -3$
* $q = -3$

(2) $q(7) = 14$
* Divide by 7: $14 / 7 = 2$
* $q = 2$

(3) $-15 = -5h$
* Divide by -5: $-15 / -5 = 3$ (Negative divided by negative is positive)
* $h = 3$

(4) $35 = a(5)$
* Divide by 5: $35 / 5 = 7$
* $a = 7$

(5) $2d = 10$
* Divide by 2: $10 / 2 = 5$
* $d = 5$

(6) $6j = 42$
* Divide by 6: $42 / 6 = 7$
* $j = 7$

(7) $\frac{1}{2}f = 5$
* Multiply by 2 (the reciprocal of $\frac{1}{2}$): $5 \times 2 = 10$
* $f = 10$

(8) $-\frac{w}{4} = -2$
* Multiply by -4: $-2 \times -4 = 8$
* $w = 8$

(9) $-42 = y(6)$
* Divide by 6: $-42 / 6 = -7$
* $y = -7$

(10) $s(-6) = -30$
* Divide by -6: $-30 / -6 = 5$
* $s = 5$

(11) $-5 = \frac{1}{5}t$
* Multiply by 5: $-5 \times 5 = -25$
* $t = -25$

(12) $8 = 2y$
* Divide by 2: $8 / 2 = 4$
* $y = 4$

Final Answer:
Part 1:
(1) h = 18
(2) g = 10
(3) w = 3
(4) g = 9
(5) i = 11
(6) w = 9
(7) z = 13
(8) m = 12
(9) x = 18
(10) d = 25
(11) k = 6
(12) s = 6

Part 2:
(1) q = -3
(2) q = 2
(3) h = 3
(4) a = 7
(5) d = 5
(6) j = 7
(7) f = 10
(8) w = 8
(9) y = -7
(10) s = 5
(11) t = -25
(12) y = 4