All categories

2 years ago

Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5)?

Mathematics

1 answer:

MrMuchimi2 years ago

8 0

The solution to the inequality is x > 3

The number line that represent the solution set will be:

<em>A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right</em>. The correct option is the second option

<h3>Linear Inequalities </h3>

From the question, we are to determine the number line that represents the solution set for the given inequality

The given inequality is

3(8 – 4x) < 6(x – 5)

First, we will solve the inequality

3(8 – 4x) < 6(x – 5)

Clear the brackets

24 - 12x < 6x - 30

Collect like terms

24 + 30 < 6x + 12x

54 < 18x

Divide both sides by 18

3 < x

∴ x > 3

Hence, the number line that represent the solution set will be:

<em>A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right</em>. The correct option is the second option

Learn more on Linear inequalities here: brainly.com/question/28003708

#SPJ1

You might be interested in

Which expression is equivalent to − 5 6 (x − 1 2 y + 12)? A) 5 6 x + 5 12 y − 10 B) 5 6 x + 5 12 y + 12 C) − 5 6 x + 5 12 y − 10

navik [9.2K]

Answer:

Option A - $-\frac{5}{6}(x-\frac{1}{2}y+12)=-\frac{5}{6}x+\frac{5}{12}y-10$

Step-by-step explanation:

Given : Expression $-\frac{5}{6}(x-\frac{1}{2}y+12)$

To find : Which expression is equivalent to given expression ?

Solution :

Expression $-\frac{5}{6}(x-\frac{1}{2}y+12)$

Applying distributive property, $a(b+c)=ab+ac$

$-\frac{5}{6}(x-\frac{1}{2}y+12)=-\frac{5}{6}x-(-\frac{5}{6})(\frac{1}{2}y)+(-\frac{5}{6})(12)$

$-\frac{5}{6}(x-\frac{1}{2}y+12)=-\frac{5}{6}x+\frac{5}{12}y-10$

Therefore, option A is correct.

7 0

3 years ago

Airline fares for a flight from Dallas to Austin are $30 for first class and $25 for tourist class. If a flight had 52 passenger

Nezavi [6.7K]

Set up 2 equations.(x = number of people in first class, y = tourist class)

30x + 25y = 1360
x + y = 52

You have 2 equations and 2 unknown. You can solve them.
I like to use the substitution method

Because y = 52 - x
Then 30x + 25(52 - x) = 1360, solve for x.

30x + 1300 - 25x = 1360
5x = 60
x = 12

Use the x to solve y
30(12) + 25y = 1360
360 + 25y = 1360
25y = 1000
y = 40

8 0

3 years ago

My brain just kind of exploded when reading this, please help!

zhannawk [14.2K]

Answer:

4.8 liters

Step-by-step explanation:

o=orange juice c=cranberry juice

Punch = 4/5o + 1/6c it means that any quantity of punch will have the same proportion of the two ingredients

now, you know that 1 liter can be written as 6/6 liters, so to get those 6/6 you multiply 1/6 by 6

for the proportion to remain valid, you must multiply by 6 also the other ingredient so (4/5)*6 = 24/5 of a liter of orange juice per liter of cranberry juice and 24/5 = 4.8 liters

4 0

3 years ago

If your starting salary is 40,000 and you receive a 3% increase at the end of every year, what is the total amount, in dollars,

Molodets [167]

Answer:

$64188.26

Step-by-step explanation:

→ Calculate the increase in decimal multiplier

( 100 + 3 ) ÷ 100 = 1.03

→ Multiply this by the salary raised to the power of 16

40000 × ( 1.03 )¹⁶

→ Solve

$64188.26

5 0

3 years ago

HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Elan Coil [88]

Answer:

see explanation

Step-by-step explanation:

The diagrams show triangular figures

The first figure has 1 dot

The second has 1 + 2 = 3 dots

The third has 3 + 3 = 6 dots

The fourth has 6 + 4 = 10 dots

Note the pattern is + 2 , + 3, + 4

Thus the fifth pattern is 10 + 5 = 15 dots

5 0

3 years ago