To solve the given two-step equations, we will isolate the unknown variable in each equation step by step. Let's go through each problem:
---
Problem 1:
\[ 6 + \frac{x}{2} = 4 \]
1. Subtract 6 from both sides:
\[
\frac{x}{2} = 4 - 6
\]
\[
\frac{x}{2} = -2
\]
2. Multiply both sides by 2 to solve for \( x \):
\[
x = -2 \times 2
\]
\[
x = -4
\]
Answer:
\[
x = -4
\]
---
Problem 2:
\[ -12x + 4 = 100 \]
1. Subtract 4 from both sides:
\[
-12x = 100 - 4
\]
\[
-12x = 96
\]
2. Divide both sides by -12:
\[
x = \frac{96}{-12}
\]
\[
x = -8
\]
Answer:
\[
x = -8
\]
---
Problem 3:
\[ -9 = -11 + \frac{x}{8} \]
1. Add 11 to both sides:
\[
-9 + 11 = \frac{x}{8}
\]
\[
2 = \frac{x}{8}
\]
2. Multiply both sides by 8:
\[
x = 2 \times 8
\]
\[
x = 16
\]
Answer:
\[
x = 16
\]
---
Problem 4:
\[ -2(d + 6) = -10 \]
1. Distribute the -2 on the left side:
\[
-2d - 12 = -10
\]
2. Add 12 to both sides:
\[
-2d = -10 + 12
\]
\[
-2d = 2
\]
3. Divide both sides by -2:
\[
d = \frac{2}{-2}
\]
\[
d = -1
\]
Answer:
\[
d = -1
\]
---
Problem 5:
\[ 5(4x + 12) = 40 \]
1. Distribute the 5 on the left side:
\[
20x + 60 = 40
\]
2. Subtract 60 from both sides:
\[
20x = 40 - 60
\]
\[
20x = -20
\]
3. Divide both sides by 20:
\[
x = \frac{-20}{20}
\]
\[
x = -1
\]
Answer:
\[
x = -1
\]
---
Problem 6:
\[ 42 + 5t = 8t \]
1. Subtract 5t from both sides:
\[
42 = 8t - 5t
\]
\[
42 = 3t
\]
2. Divide both sides by 3:
\[
t = \frac{42}{3}
\]
\[
t = 14
\]
Answer:
\[
t = 14
\]
---
Problem 7:
\[ \frac{1}{3}c - 7 = 1 \]
1. Add 7 to both sides:
\[
\frac{1}{3}c = 1 + 7
\]
\[
\frac{1}{3}c = 8
\]
2. Multiply both sides by 3:
\[
c = 8 \times 3
\]
\[
c = 24
\]
Answer:
\[
c = 24
\]
---
Problem 8:
\[ \frac{k}{-3} + 3 = -2 \]
1. Subtract 3 from both sides:
\[
\frac{k}{-3} = -2 - 3
\]
\[
\frac{k}{-3} = -5
\]
2. Multiply both sides by -3:
\[
k = -5 \times (-3)
\]
\[
k = 15
\]
Answer:
\[
k = 15
\]
---
Final Answers:
\[
\boxed{
\begin{array}{ll}
x = -4 & x = -8 \\
x = 16 & d = -1 \\
x = -1 & t = 14 \\
c = 24 & k = 15
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of 100 steps worksheet.
