Basic Algebra Worksheets - Free Printable

Problem: Solve the linear equations from the worksheet.

#### 1 a. $ -3 = 7p - 5 $

Step-by-Step Solution:
1. Start with the equation:
\[
-3 = 7p - 5
\]
2. Add 5 to both sides to isolate the term with \( p \):
\[
-3 + 5 = 7p - 5 + 5
\]
\[
2 = 7p
\]
3. Divide both sides by 7 to solve for \( p \):
\[
\frac{2}{7} = p
\]

Final Answer:
\[
\boxed{\frac{2}{7}}
\]

---

#### 1 b. $ \frac{-5 - v}{3} = -1 $

Step-by-Step Solution:
1. Start with the equation:
\[
\frac{-5 - v}{3} = -1
\]
2. Multiply both sides by 3 to eliminate the denominator:
\[
3 \cdot \frac{-5 - v}{3} = -1 \cdot 3
\]
\[
-5 - v = -3
\]
3. Add 5 to both sides to isolate the term with \( v \):
\[
-5 + 5 - v = -3 + 5
\]
\[
-v = 2
\]
4. Multiply both sides by -1 to solve for \( v \):
\[
v = -2
\]

Final Answer:
\[
\boxed{-2}
\]

---

#### 2 a. $ 7 = \frac{w - (-7)}{5} $

Step-by-Step Solution:
1. Simplify the expression inside the numerator:
\[
w - (-7) = w + 7
\]
So the equation becomes:
\[
7 = \frac{w + 7}{5}
\]
2. Multiply both sides by 5 to eliminate the denominator:
\[
5 \cdot 7 = \frac{w + 7}{5} \cdot 5
\]
\[
35 = w + 7
\]
3. Subtract 7 from both sides to solve for \( w \):
\[
35 - 7 = w + 7 - 7
\]
\[
w = 28
\]

Final Answer:
\[
\boxed{28}
\]

---

#### 2 b. $ -1 - 4s = 8 $

Step-by-Step Solution:
1. Start with the equation:
\[
-1 - 4s = 8
\]
2. Add 1 to both sides to isolate the term with \( s \):
\[
-1 + 1 - 4s = 8 + 1
\]
\[
-4s = 9
\]
3. Divide both sides by -4 to solve for \( s \):
\[
s = \frac{9}{-4}
\]
\[
s = -\frac{9}{4}
\]

Final Answer:
\[
\boxed{-\frac{9}{4}}
\]

---

#### 3 a. $ 2 = 3 - 2t $

Step-by-Step Solution:
1. Start with the equation:
\[
2 = 3 - 2t
\]
2. Subtract 3 from both sides to isolate the term with \( t \):
\[
2 - 3 = 3 - 3 - 2t
\]
\[
-1 = -2t
\]
3. Divide both sides by -2 to solve for \( t \):
\[
t = \frac{-1}{-2}
\]
\[
t = \frac{1}{2}
\]

Final Answer:
\[
\boxed{\frac{1}{2}}
\]

---

#### 3 b. $ 9 = \frac{5 - t}{-5} $

Step-by-Step Solution:
1. Start with the equation:
\[
9 = \frac{5 - t}{-5}
\]
2. Multiply both sides by -5 to eliminate the denominator:
\[
9 \cdot (-5) = \frac{5 - t}{-5} \cdot (-5)
\]
\[
-45 = 5 - t
\]
3. Subtract 5 from both sides to isolate the term with \( t \):
\[
-45 - 5 = 5 - 5 - t
\]
\[
-50 = -t
\]
4. Multiply both sides by -1 to solve for \( t \):
\[
t = 50
\]

Final Answer:
\[
\boxed{50}
\]

---

Final Answers:

1. a. $\boxed{\frac{2}{7}}$
1. b. $\boxed{-2}$
2. a. $\boxed{28}$
2. b. $\boxed{-\frac{9}{4}}$
3. a. $\boxed{\frac{1}{2}}$
3. b. $\boxed{50}$