222,491 views
2 votes
2 votes
How many solutions exist for the given equation?

12x + 1 = 3(4x + 1) - 2
zero
one
two
infinitely many

User Paul Hodgson
by
2.6k points

2 Answers

22 votes
22 votes

Answer:

A.

Explanation:

User Jesper Nordenberg
by
2.9k points
8 votes
8 votes

Answer:

Zero

Explanation:

Simplifying

12x + 1 = 3(4x + 1) + -2

Reorder the terms:

1 + 12x = 3(4x + 1) + -2

Reorder the terms:

1 + 12x = 3(1 + 4x) + -2

1 + 12x = (1 * 3 + 4x * 3) + -2

1 + 12x = (3 + 12x) + -2

Reorder the terms:

1 + 12x = 3 + -2 + 12x

Combine like terms: 3 + -2 = 1

1 + 12x = 1 + 12x

Add '-1' to each side of the equation.

1 + -1 + 12x = 1 + -1 + 12x

Combine like terms: 1 + -1 = 0

0 + 12x = 1 + -1 + 12x

12x = 1 + -1 + 12x

Combine like terms: 1 + -1 = 0

12x = 0 + 12x

12x = 12x

Add '-12x' to each side of the equation.

12x + -12x = 12x + -12x

Combine like terms: 12x + -12x = 0

0 = 12x + -12x

Combine like terms: 12x + -12x = 0

0 = 0

Solving

0 = 0

Couldn't find a variable to solve for.

This equation is an identity, all real numbers are solutions.

User Andrew Zimmer
by
3.1k points
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