The image you provided is a worksheet focused on solving simple algebraic equations. The task involves filling in the blanks to complete each equation. Below, I will solve each problem step by step and explain the solution.
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Worksheet Problems and Solutions
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1. Solve for \( x \):
-
Equation: \( 3 + x = 4 \)
-
Solution:
- Subtract 3 from both sides:
\[
x = 4 - 3
\]
\[
x = 1
\]
-
Answer: \( x = 1 \)
####
2. Solve for \( y \):
-
Equation: \( y + 0 = 14 \)
-
Solution:
- Adding 0 to any number does not change its value:
\[
y = 14
\]
-
Answer: \( y = 14 \)
####
3. Solve for \( z \):
-
Equation: \( 4 + z = 2 \)
-
Solution:
- Subtract 4 from both sides:
\[
z = 2 - 4
\]
\[
z = -2
\]
-
Answer: \( z = -2 \)
####
4. Solve for \( w \):
-
Equation: \( w + 7 = 11 \)
-
Solution:
- Subtract 7 from both sides:
\[
w = 11 - 7
\]
\[
w = 4
\]
-
Answer: \( w = 4 \)
####
5. Solve for \( x \):
-
Equation: \( 3x = 12 \)
-
Solution:
- Divide both sides by 3:
\[
x = \frac{12}{3}
\]
\[
x = 4
\]
-
Answer: \( x = 4 \)
####
6. Solve for \( y \):
-
Equation: \( y - 5 = -2 \)
-
Solution:
- Add 5 to both sides:
\[
y = -2 + 5
\]
\[
y = 3
\]
-
Answer: \( y = 3 \)
####
7. Solve for \( z \):
-
Equation: \( z + 2 = 3 \)
-
Solution:
- Subtract 2 from both sides:
\[
z = 3 - 2
\]
\[
z = 1
\]
-
Answer: \( z = 1 \)
####
8. Solve for \( w \):
-
Equation: \( 2w = 6 \)
-
Solution:
- Divide both sides by 2:
\[
w = \frac{6}{2}
\]
\[
w = 3
\]
-
Answer: \( w = 3 \)
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Final Answers:
1. \( x = 1 \)
2. \( y = 14 \)
3. \( z = -2 \)
4. \( w = 4 \)
5. \( x = 4 \)
6. \( y = 3 \)
7. \( z = 1 \)
8. \( w = 3 \)
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Explanation of the Process:
Each problem involves isolating the variable (e.g., \( x \), \( y \), \( z \), or \( w \)) on one side of the equation. This is done using basic algebraic operations such as addition, subtraction, multiplication, or division. The goal is to balance the equation so that the variable is alone on one side, with its value clearly determined.
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Final Answer Boxed:
\[
\boxed{x = 1, y = 14, z = -2, w = 4, x = 4, y = 3, z = 1, w = 3}
\]
Parent Tip: Review the logic above to help your child master the concept of algebraic expressions worksheet 5th grade.
