The task involves solving a series of linear equations in one variable. Each equation can be solved by isolating the variable on one side of the equation. Let's solve each equation step by step.
---
Equation 1: \( x + 2.3 = 4.5 \)
To isolate \( x \), subtract 2.3 from both sides:
\[
x + 2.3 - 2.3 = 4.5 - 2.3
\]
\[
x = 2.2
\]
Answer: \( x = 2.2 \)
---
Equation 2: \( x - 2.3 = 4.5 \)
To isolate \( x \), add 2.3 to both sides:
\[
x - 2.3 + 2.3 = 4.5 + 2.3
\]
\[
x = 6.8
\]
Answer: \( x = 6.8 \)
---
Equation 3: \( y - 12.5 = 14 \)
To isolate \( y \), add 12.5 to both sides:
\[
y - 12.5 + 12.5 = 14 + 12.5
\]
\[
y = 26.5
\]
Answer: \( y = 26.5 \)
---
Equation 4: \( y + 12.5 = 14 \)
To isolate \( y \), subtract 12.5 from both sides:
\[
y + 12.5 - 12.5 = 14 - 12.5
\]
\[
y = 1.5
\]
Answer: \( y = 1.5 \)
---
Equation 5: \( 6.5 = m - 3.1 \)
To isolate \( m \), add 3.1 to both sides:
\[
6.5 + 3.1 = m - 3.1 + 3.1
\]
\[
m = 9.6
\]
Answer: \( m = 9.6 \)
---
Equation 6: \( 6.5 = m + 3.1 \)
To isolate \( m \), subtract 3.1 from both sides:
\[
6.5 - 3.1 = m + 3.1 - 3.1
\]
\[
m = 3.4
\]
Answer: \( m = 3.4 \)
---
Equation 7: \( c + 4.5 = 9.8 \)
To isolate \( c \), subtract 4.5 from both sides:
\[
c + 4.5 - 4.5 = 9.8 - 4.5
\]
\[
c = 5.3
\]
Answer: \( c = 5.3 \)
---
Equation 8: \( c - 4.5 = 9.8 \)
To isolate \( c \), add 4.5 to both sides:
\[
c - 4.5 + 4.5 = 9.8 + 4.5
\]
\[
c = 14.3
\]
Answer: \( c = 14.3 \)
---
Equation 9: \( f - 3.5 = 6.7 \)
To isolate \( f \), add 3.5 to both sides:
\[
f - 3.5 + 3.5 = 6.7 + 3.5
\]
\[
f = 10.2
\]
Answer: \( f = 10.2 \)
---
Equation 10: \( f + 3.5 = 6.7 \)
To isolate \( f \), subtract 3.5 from both sides:
\[
f + 3.5 - 3.5 = 6.7 - 3.5
\]
\[
f = 3.2
\]
Answer: \( f = 3.2 \)
---
Final Answers:
\[
\boxed{
\begin{array}{ll}
1) & x = 2.2 \\
2) & x = 6.8 \\
3) & y = 26.5 \\
4) & y = 1.5 \\
5) & m = 9.6 \\
6) & m = 3.4 \\
7) & c = 5.3 \\
8) & c = 14.3 \\
9) & f = 10.2 \\
10) & f = 3.2 \\
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of solving equations with one variable worksheet.
