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3 years ago

What is the solution of |2x + 3| = 3x + 5?

Mathematics

2 answers:

Elanso [62]3 years ago

5 0

Answer:

$x=-\frac{8}{5}$

Step-by-step explanation:

The given absolute value equation is

$|2x+3|=3x+5$

This implies that;

$-(2x+3)=3x+5\:or\:2x+3=3x+5$

$-2x-3=3x+5\:or\:2x+3=3x+5$

Group similar terms in both equations;

$-2x-3x=5+3\:or\:2x-3x=5-3$

$-5x=8\:or\:-x=-2$

$x=-\frac{8}{5}\:or\:x=2$

CHECK

$|2(2)+3|=3(2)+5$

$|4+3|=6+5$

$7=11$ .

This false. Hence x=2 is an extraneous solution.

When $x=-\frac{8}{5}$

$|2(-\frac{8}{5})+3|=3(-\frac{8}{5})+5$

$|-\frac{16}{5}+3|=(-\frac{24}{5})+5$

$|-\frac{1}{5}|=\frac{1}{5}$

$\frac{1}{5}=\frac{1}{5}$

This statement is true

tekilochka [14]3 years ago

4 0

<h2>Answer:</h2>

<u>The right answer is </u><u>x = -8/5</u>

<h2>Step-by-step explanation:</h2>

See the attached figure

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Step-by-step explanation:

<u>Geometric Sequences</u>

There are two basic types of sequences: arithmetic and geometric. The arithmetic sequences can be recognized because each term is found as the previous term plus a fixed number called the common difference.

In the geometric sequences, each term is found by multiplying (or dividing) the previous term by a fixed number, called the common ratio.

We are given the sequence:

112, -28, 7, ...

It's easy to find out this is a geometric sequence because the signs of the terms are alternating. If it was an arithmetic sequence, the third term should be negative like the second term.

Let's find the common ratio by dividing each term by the previous term:

$\displaystyle r=\frac{-28}{112}=-\frac{1}{4}$

Testing with the third term:

$\displaystyle -28*-\frac{1}{4}=7$

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