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Use a General Strategy to Solve Linear Equations: example 2.45 · Physics Playground

Exercises Equations and inequalities

Example 2.45 from Elementary Algebra, 2.4 Use a General Strategy to Solve Linear Equations

Use a General Strategy to Solve Linear Equations: example 2.45

Classify the equation as a conditional equation, an identity, or a contradiction. Then state the solution.

$6 (2 n - 1) + 3 = 2 n - 8 + 5 (2 n + 1)$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution

Distribute.

Combine like terms.

Subtract $12 n$ to get the $n$ ’s to one side.

Simplify.

This is a true statement. The equation is an identity.
The solution is all real numbers.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Classify the equation as a conditional equation, an identity, or a contradiction and then state the solution:

$4 + 9 (3 x - 7) = −42 x - 13 + 23 (3 x - 2)$

How did it go?

PreviousUse a General Strategy to Solve Linear Equations: example 2.44 Next Use a General Strategy to Solve Linear Equations: example 2.46

From Elementary Algebra (1st edition) by OpenStax (Rice University), section 2.4, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.


Distribute.
Combine like terms.
Subtract $12 n$ to get the $n$ ’s to one side.
Simplify.
This is a true statement.	The equation is an identity. The solution is all real numbers.

Solution

Your turn