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Name:
RECOGNIZING STRUCTURE TO SOLVE TWO STEP EQUATIONS
N-GEN MATH HOMEWORK
Fluency
1. Which of the following is the solution to: ?
(1)
(3)
(2)
(4)
2. Which value below solves the equation: ?
(1)
(3)
(2)
(4)
3. Solve each of the following equations in two different ways: (1) by reversing the order of operations and (2) by using the distributive property to simplify the left-hand side.
(a)
Method (1)
Method (2)
(b)
Method (1)
Method (2)
N-Gen Matis 7, Unit 6-Linear Equations and Inequalties - Lesson 5
eMATHinstruction, RED HooK, NY 12571, 02020
Studdy Solution
STEP 1
1. We are solving two-step linear equations.
2. The problems involve basic algebraic manipulations such as distribution, addition, subtraction, multiplication, and division.
3. We are tasked with solving each equation using two different methods where applicable.
STEP 2
1. Solve the equation using basic algebraic manipulation.
2. Solve the equation using basic algebraic manipulation.
3. Solve the equation using two methods: reversing the order of operations and using the distributive property.
4. Solve the equation using two methods: reversing the order of operations and using the distributive property.
STEP 3
Solve the equation .
- Divide both sides by 5 to isolate the term with :
x+7 = \frac{50}{5}
\]
x+7 = 10
\]
- Subtract 7 from both sides to solve for :
x = 10 - 7
\]
x = 3
\]
The solution is .
STEP 4
Solve the equation .
- Multiply both sides by 2 to eliminate the fraction:
n-6 = 4 \times 2
\]
n-6 = 8
\]
- Add 6 to both sides to solve for :
n = 8 + 6
\]
n = 14
\]
The solution is .
STEP 5
Solve the equation using two methods.
Method (1): Reversing the order of operations
- Divide both sides by 5:
x+3 = \frac{45}{5}
\]
x+3 = 9
\]
- Subtract 3 from both sides:
x = 9 - 3
\]
x = 6
\]
Method (2): Using the distributive property
- Distribute the 5:
$ 5x + 15 = 45
\]
- Subtract 15 from both sides:
5x = 45 - 15
\]
5x = 30
\]
- Divide by 5:
x = \frac{30}{5}
\]
x = 6
\]
The solution is .
STEP 6
Solve the equation using two methods.
Method (1): Reversing the order of operations
- Divide both sides by 3:
n-7 = \frac{27}{3}
\]
n-7 = 9
\]
- Add 7 to both sides:
n = 9 + 7
\]
n = 16
\]
Method (2): Using the distributive property
- Distribute the 3:
$ 3n - 21 = 27
\]
- Add 21 to both sides:
3n = 27 + 21
\]
3n = 48
\]
- Divide by 3:
n = \frac{48}{3}
\]
n = 16
\]
The solution is .
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