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Pre-algebra

Ron Larson, Laurie Boswell, Timothy D. Kanold, Lee Stiff

$Math Studyset Vaia Explanations$ Math

Common Core Edition · 183 pages

ISBN: 9780547587776

Chapter 3: Q2. (page 133)

Explain why the equation 5z + 2 = 5z has no solution.

Short Answer

Expert verified

The equation $5 z + 2 = 5 z$ has no solution because if we cancel 5z from both sides then we get 2 = 0, which is not true.

Step by step solution

01

Step-1 – Given

The given equation is $5 z + 2 = 5 z$ .

02

Step-2 – To determine

We have to find the reason why the equation $5 z + 2 = 5 z$ has no solution.

03

Step-3 – Calculation

We try to solve the given equation for z, if possible

$\begin{array}{l} 5 z + 2 = 5 z [Theoriginalequation.] \\ 5 z + 2 - 5 z = 5 z - 5 z [Subtract5 z fromeachside.] \\ 2 = 0 [Simplify.] \end{array}$

The statement $2 = 0$ is false, so the equation has no solution.

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