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Big Ideas Math: Modeling Real Life, Grade 7

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Big Ideas Math: Modeling Real Life, Grade 7 View details

Practice Test

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Exercise 2 Page 176

Gather all of the variable terms on one side of the equation and all of the constant terms on the other side.

x=- 2

To solve an equation, we should first gather all of the variable terms on one side and all of the constant terms on the other side using the Properties of Equality. In this case, we need to start by using the Distributive Property to simplify the left- and right-hand sides of the equation.

2(x+1)=- 2

Distribute 2

2x+2(1)=- 2

Identity Property of Multiplication

2x+2=- 2

Now, we can continue to solve using the Properties of Equality.

2x+2=- 2

LHS-2=RHS-2

2x+2-2=- 2-2

Subtract term

2x=- 4

.LHS /2.=.RHS /2.

2x/2=- 4/2

▼

Simplify left-hand side

MovePartNumRight

a* b/c=a/c* b

2/2x=- 4/2

a/a=1

1x=- 4/2

Identity Property of Multiplication

x=- 4/2

▼

Simplify right-hand side

MoveNegNumToFrac

Put minus sign in front of fraction

x=- 4/2

Calculate quotient

x=- 2

The solution to the equation is x=- 2. We can check our solution by substituting it into the original equation.

2(x+1)=- 2

x= - 2

2( - 2+1) ? = - 2

▼

Simplify

Add terms

2(- 1)? = - 2

a(- b)=- a * b

- 2( 1)? = - 2

Identity Property of Multiplication

- 2=- 2

Since the left-hand side is equal to the right-hand side, our solution is correct.

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Are you having trouble learning how to solve equations? Would you like to see why the Properties of Equality work? Do real-world examples help you understand more about the why and how of math topics? If you answered Yes to any of these questions, check out the Mathleaks courses related to this topic!