Problem: Solve the linear equations from the worksheet.
####
Equation 1a:
$$
-9 \cdot 7 = 8(y - 6.6)
$$
Step-by-Step Solution:
1. Simplify the left-hand side:
$$
-9 \cdot 7 = -63
$$
So the equation becomes:
$$
-63 = 8(y - 6.6)
$$
2. Distribute the 8 on the right-hand side:
$$
-63 = 8y - 52.8
$$
3. Isolate the term with \( y \) by adding 52.8 to both sides:
$$
-63 + 52.8 = 8y
$$
$$
-10.2 = 8y
$$
4. Solve for \( y \) by dividing both sides by 8:
$$
y = \frac{-10.2}{8}
$$
$$
y = -1.275
$$
Final Answer for 1a:
$$
\boxed{-1.275}
$$
---
####
Equation 1b:
$$
8(t + 5) + 2 = 4.8t + 4
$$
Step-by-Step Solution:
1. Distribute the 8 on the left-hand side:
$$
8t + 40 + 2 = 4.8t + 4
$$
Simplify the left-hand side:
$$
8t + 42 = 4.8t + 4
$$
2. Subtract \( 4.8t \) from both sides to get all \( t \)-terms on one side:
$$
8t - 4.8t + 42 = 4
$$
$$
3.2t + 42 = 4
$$
3. Subtract 42 from both sides to isolate the term with \( t \):
$$
3.2t = 4 - 42
$$
$$
3.2t = -38
$$
4. Solve for \( t \) by dividing both sides by 3.2:
$$
t = \frac{-38}{3.2}
$$
Simplify the division:
$$
t = -11.875
$$
Final Answer for 1b:
$$
\boxed{-11.875}
$$
---
####
Equation 2a:
$$
6 \cdot (-9) = 9.5(a - 6.9)
$$
Step-by-Step Solution:
1. Simplify the left-hand side:
$$
6 \cdot (-9) = -54
$$
So the equation becomes:
$$
-54 = 9.5(a - 6.9)
$$
2. Distribute the 9.5 on the right-hand side:
$$
-54 = 9.5a - 63.45
$$
3. Add 63.45 to both sides to isolate the term with \( a \):
$$
-54 + 63.45 = 9.5a
$$
$$
9.45 = 9.5a
$$
4. Solve for \( a \) by dividing both sides by 9.5:
$$
a = \frac{9.45}{9.5}
$$
Simplify the division:
$$
a = 0.9947 \quad (\text{approximately})
$$
Final Answer for 2a:
$$
\boxed{0.995}
$$
---
####
Equation 2b:
$$
2(a - 8.5) - 2.6 = 3.1a + 7.4
$$
Step-by-Step Solution:
1. Distribute the 2 on the left-hand side:
$$
2a - 17 - 2.6 = 3.1a + 7.4
$$
Simplify the left-hand side:
$$
2a - 19.6 = 3.1a + 7.4
$$
2. Subtract \( 2a \) from both sides to get all \( a \)-terms on one side:
$$
-19.6 = 3.1a - 2a + 7.4
$$
$$
-19.6 = 1.1a + 7.4
$$
3. Subtract 7.4 from both sides to isolate the term with \( a \):
$$
-19.6 - 7.4 = 1.1a
$$
$$
-27 = 1.1a
$$
4. Solve for \( a \) by dividing both sides by 1.1:
$$
a = \frac{-27}{1.1}
$$
Simplify the division:
$$
a = -24.545 \quad (\text{approximately})
$$
Final Answer for 2b:
$$
\boxed{-24.55}
$$
---
Final Answers:
1.
1a: $\boxed{-1.275}$
2.
1b: $\boxed{-11.875}$
3.
2a: $\boxed{0.995}$
4.
2b: $\boxed{-24.55}$
Parent Tip: Review the logic above to help your child master the concept of graphing linear equations worksheet 8th grade.
