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Westkost [7]
3 years ago
8

Solve absolute value equation. Check for extraneous solution. |2x-3|=2x-1. Post it into the drop box for the unit 2 review.

Mathematics
1 answer:
polet [3.4K]3 years ago
6 0

let's keep in mind that, an absolute value expression is in effect a piecewise one, since it has a ± versions of it.


\bf |2x-3|=2x-1\implies \begin{cases}+(2x-3)=2x-1\\-(2x-3)=2x-1\end{cases}\\\\[-0.35em]~\dotfill\\\\+(2x-3)=2x-1\implies 2x-3=2x-1\implies -3 \ne -1\impliedby extraneous\\\\[-0.35em]~\dotfill\\\\-(2x-3)=2x-1\implies 2x-3=-2x+1\implies 4x=4\\\\\\x=\cfrac{4}{4}\implies x=1

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Answer:

1)

a) 6x+3 = 27

b) x=4

c) We know that x is price of each ticket, so The price of each ticket is $4. They bought 6 tickets, so total cost of ticket = 24 and $3 for parking so, total money spent = $27.

2)

a) 3x + 6 = 27

b) x= 7

c) We know that x is amount of juice poured, so 3 friends of Diego will get 7 ounces of Juice, while Diego will get 6 ounces of juice.

3)

a) 27x + 3 = 6

b) x= 1/9

c) We know that x is time spend on each picture, so Jada spend 1/9 hour on each picture

Step-by-step explanation:

1. A family buys 6 tickets to a show. They also pay a $3 parking fee. They spend $27 to see the  show.

a)  Decide which equation represents each story. What does x represent in each equation?

Let x be price of one ticket.

The equation will be: 6x+3 = 27

b. Find the solution to each equation. Explain or show your reasoning,

Now solving the equation:

6x+3=27

6x=27-3

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x=24/6

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So, we get x = 4

c. What does each solution tell you about its situation?

We know that x is price of each ticket, so The price of each ticket is $4. They bought 6 tickets, so total cost of ticket = 24 and $3 for parking so, total money spent = $27.

2. Diego has 27 ounces of juice. He pours equal amounts for each of his 3 friends and has 6  ounces left for himself.

a)  Decide which equation represents each story. What does x represent in each equation?

Let x be amount of juice poured.

The equation will be: 3x+6 = 27

b. Find the solution to each equation. Explain or show your reasoning,

Now solving the equation:

3x+6=27

3x=27-6

3x=21

x=21/3

x=7

So, we get x = 7

c. What does each solution tell you about its situation?

We know that x is amount of juice poured, so 3 friends of Diego will get 7 ounces of Juice, while Diego will get 6 ounces of juice.

3. Diego has 27 ounces of juice. He pours equal amounts for each of his 3 friends and has 6  ounces left for himself.

a)  Jada works for 6 hours preparing for the art fair. She spends 3 hours on a sculpture and  then paints 27 picture frames.

Let x be time spend on each picture frame.

The equation will be: 27x+3=6

b. Find the solution to each equation. Explain or show your reasoning,

Now solving the equation:

27x+3=6

27x=6-3

27x=3

x=3/27

x=1/9

So, we get x = 1/9

c. What does each solution tell you about its situation?

We know that x is time spend on each picture, so Jada spend 1/9 hour on each picture

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