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Exercises Equations and inequalities

Example 2.47 from Elementary Algebra, 2.4 Use a General Strategy to Solve Linear Equations

Use a General Strategy to Solve Linear Equations: example 2.47

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

$5 m + 3 (9 + 3 m) = 2 (7 m - 11)$

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 $14 m$ from both sides.

Simplify.

But $27 \neq −22$ . The equation is a contradiction.
It has no solution.

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:

$12 c + 5 (5 + 3 c) = 3 (9 c - 4)$

How did it go?

PreviousUse a General Strategy to Solve Linear Equations: example 2.46 Next Solve Equations with Fractions or Decimals: example 2.48

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.