All categories

2 years ago

Which represents the solution to the absolute value equation? 3|2x+4|-1=11

1 answer:

5 0

The first step for absolute value equations is to isolate the expression contained within the absolute value bars:

3|2x+4|-1 = 11
3|2x+4| = 12
|2x+4| = 4

so |2x+4| is 4 units away from 0 on a number line, but we don't know in which direction -- negative or positive? you'll have two answers.

2x+4 = 4

AND

2x+4 = -4

solve both of those two step equations and you'll get

x = 0

AND

x = -4

so 0 and -4 are your solutions.

You might be interested in

5. Show that the following points are collinear. a) (1, 2), (4, 5), (8,9)

Irina-Kira [14]

Label the points A,B,C

A = (1,2)
B = (4,5)
C = (8,9)

Let's find the distance from A to B, aka find the length of segment AB.

We use the distance formula.

$A = (x_1,y_1) = (1,2) \text{ and } B = (x_2, y_2) = (4,5)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(1-4)^2 + (2-5)^2}\\\\d = \sqrt{(-3)^2 + (-3)^2}\\\\d = \sqrt{9 + 9}\\\\d = \sqrt{18}\\\\d = \sqrt{9*2}\\\\d = \sqrt{9}*\sqrt{2}\\\\d = 3\sqrt{2}\\\\$

Segment AB is exactly $3\sqrt{2}$ units long.

Now let's find the distance from B to C

$B = (x_1,y_1) = (4,5) \text{ and } C = (x_2, y_2) = (8,9)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(4-8)^2 + (5-9)^2}\\\\d = \sqrt{(-4)^2 + (-4)^2}\\\\d = \sqrt{16 + 16}\\\\d = \sqrt{32}\\\\d = \sqrt{16*2}\\\\d = \sqrt{16}*\sqrt{2}\\\\d = 4\sqrt{2}\\\\$

Segment BC is exactly $4\sqrt{2}$ units long.

Adding these segments gives

$AB+BC = 3\sqrt{2}+4\sqrt{2} = 7\sqrt{2}$

----------------------

Now if A,B,C are collinear then AB+BC should get the length of AC.

AB+BC = AC

Let's calculate the distance from A to C

$A = (x_1,y_1) = (1,2) \text{ and } C = (x_2, y_2) = (8,9)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(1-8)^2 + (2-9)^2}\\\\d = \sqrt{(-7)^2 + (-7)^2}\\\\d = \sqrt{49 + 49}\\\\d = \sqrt{98}\\\\d = \sqrt{49*2}\\\\d = \sqrt{49}*\sqrt{2}\\\\d = 7\sqrt{2}\\\\$

AC is exactly $7\sqrt{2}$ units long.

Therefore, we've shown that AB+BC = AC is a true equation.

This proves that A,B,C are collinear.

For more information, check out the segment addition postulate.

7 0

2 years ago

Help pls me i need help with math

Ymorist [56]

Answer:

11 yd

Step-by-step explanation:

16-5=11 yd

6 0

2 years ago

Read 2 more answers

61 = r/3 − 7 what is r

WINSTONCH [101]

Answer: r = -244

Step-by-step explanation:

3 0

2 years ago

PLEASE EXPLAIN and Help me solve this<br> thank you!!!

Nina [5.8K]

Answer:

it could be drawn using maths

3 0

3 years ago

Guys I need the right answer ASAP PLZ read the question and give me a STEP BY STEP EXPLANATION with the correct answer plz I nee

Gwar [14]

Answer:

Number 3

Step-by-step explanation:

The reason this is so is because he is looking for the amount of peaches he can buy. The equation that is number one represents that because it say 3.18 + 1.19p ≤ 10.00 showing that he wants an amount of peaches that costs less than 10.00. 1.19p standing for the amount of peaches and 3.18 representing the pomegranates.

5 0

3 years ago