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Sliva [168]
4 years ago
7

Two and four tenths times a number minus three is greater than one and six tenths times the number minus four and one tenth

Mathematics
1 answer:
diamong [38]4 years ago
8 0

Let's first turn all the words into numbers:

Two and four tenths = 2.4

One and six tenths = 1.6

Four and one tenth = 4.1

Now lets represent "a number" as x.

Then translate the wording into a linear equation:

2.4x-3>1.6x-4.1

Simplify and isolate the variable:

0.8x>-1.1

Divide by 0.8

x>1.375 or x>1 3/8

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Answer:

<h2>w = -8</h2>

Step-by-step explanation:

Given the equation solved by Ernesto expressed as \sqrt{\dfrac{1}{2}w+8}=-2, the extraneous solution obtained by Ernesto is shown below;

\sqrt{\dfrac{1}{2}w+8}=-2\\\\square\ both \ sides \ of \ the \ equation\\(\sqrt{\dfrac{1}{2}w+8})^2=(-2)^2\\\\\dfrac{1}{2}w+8 = 4\\\\Subtract \ 8 \ from \ both \ sides\\\\\dfrac{1}{2}w+8 - 8= 4- 8\\\\\dfrac{1}{2}w= -4\\\\multiply \ both \ sides \ by \ 2\\\\\dfrac{1}{2}w*2= -4*2\\\\w = -8

Hence, the extraneous solution that Ernesto obtained is w = -8

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