Question: "To calculate: The solution set of |2v+5|=|2v−1|."

smismSitlougsyy

Answered question

2021-11-13

To calculate: The solution set of

| 2 v + 5 | = | 2 v - 1 |

soniarus7x

Beginner2021-11-14Added 17 answers

Given Information:
The absolute value inequality is

| 2 v + 5 | = | 2 v - 1 |

.
Formula Used:
From the definition of absolute value,

| u | = k

is equivalent to

u = k

u = - k

Calculation:
The given inequality is

| 2 v + 5 | = | 2 v — 1 |

The inequality is in the form

| u | = k

, where

u = 2 v - 1

. Write the equivalent compound inequality,

2 v + 5 = 2 v - 1

2 v - 2 v = - 5 - 1

0 \neq - 6

Or,

2 v + 5 = - (2 v - 1)

2 v + 5 = - 2 v + l

Check at

v = — 1

| 2 v + 5 | = | 2 v - 1 |

| 2 (- 1) + 5 | | 2 (- 1) - 1 |

| - 2 + 5 | | - 2 - 1 |

3 = 3

The left side value is equal to the right-side value. Thus, the value

v = - 1

is verified.
Therefore, the solution set of

| p — 4 | = | 2 p — 3 |

{- 1}

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