Question
What is the solution of 0.2x-4-2x < -0.4 and 3x+2.7 < 3
- x < -2
- x <0.1
- x < 1
- x > -2 and x < 0.1
- x > -2 and x <1
Hint:
If two real numbers or algebraic expressions are related by the symbols “>”, “<”, “≥”, “≤”, then the relation is called an inequality. For example, x>5 (x should be greater than 5).
A compound inequality is a sentence with two inequality statements joined either by the word “or” or by the word “and.” “And” indicates that both statements of the compound sentence are true at the same time. “Or” indicates that, as long as either statement is true, the entire compound sentence is true.
If the symbol is (≥ or ≤) then you fill in the dot and if the symbol is (> or <) then you do not fill in the dot.
The correct answer is: x > -2 and x < 0.1
Solving 0.2x-4-2x < -0.4
-4 - 1.8 x < -0.4
-1.8 x < 3.6
x > -2
Solving 3x+2.7 < 3
3x < 0.
x < 0.1
Final Answer:
The solution for 0.2x-4-2x < -0.4 and 3x+2.7 < 3 is x > -2 and x < 0.1. Hence, option d is correct.
Solving 3x+2.7 < 3
Final Answer:
The solution for 0.2x-4-2x < -0.4 and 3x+2.7 < 3 is x > -2 and x < 0.1. Hence, option d is correct.
Related Questions to study
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To get from point A to point B you must avoid walking through a pond. To avoid the pond, you must walk 34 meters south and 41 meters east. To the nearest meter, how many meters would be saved if it were possible to walk through the pond?
To get from point A to point B you must avoid walking through a pond. To avoid the pond, you must walk 34 meters south and 41 meters east. To the nearest meter, how many meters would be saved if it were possible to walk through the pond?
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Identify the kind of sentence Orange did not go to school as it was raining.
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Volunteers at an animal shelter are building a rectangular dog run so that one shorter side of the rectangle is formed by the shelter building as shown. They plan to spend between $100 and $200 on fencing for the sides at a cost of $2.50 per ft. write and solve a compound inequality to model the possible length of the dog run.
Follow the same steps as when solving equations to solve compound inequalities. However, because compound inequalities are composed of two inequalities, separate them and solve each inequity separately. Once the inequalities are separated, isolate the variable using the inverse operation, similar to how equations are solved.
For example, to solve the compound inequality 14 > 2x > 4, do the following:
14 > 2x > 4
The two inequalities are separated by 14 > 2x and 2x > 4.
To isolate the variable, divide both sides by 2: 14/2 > 2x/2 and 2x/2 > 4/2.
7 > x and x > 2 are now two sets of solutions.
7 > x > 2, the possible answers range from 2 to 7.
Volunteers at an animal shelter are building a rectangular dog run so that one shorter side of the rectangle is formed by the shelter building as shown. They plan to spend between $100 and $200 on fencing for the sides at a cost of $2.50 per ft. write and solve a compound inequality to model the possible length of the dog run.
Follow the same steps as when solving equations to solve compound inequalities. However, because compound inequalities are composed of two inequalities, separate them and solve each inequity separately. Once the inequalities are separated, isolate the variable using the inverse operation, similar to how equations are solved.
For example, to solve the compound inequality 14 > 2x > 4, do the following:
14 > 2x > 4
The two inequalities are separated by 14 > 2x and 2x > 4.
To isolate the variable, divide both sides by 2: 14/2 > 2x/2 and 2x/2 > 4/2.
7 > x and x > 2 are now two sets of solutions.
7 > x > 2, the possible answers range from 2 to 7.
A peanut company ships its product in a carton that weighs 20 oz when empty. Twenty bags of peanuts are shipped in each carton. The acceptable weight for one bag of peanuts is between 30.5 oz and 33.5 oz, inclusive. If a carton weighs too much or too little, it is opened for inspection. Write and solve a compound inequality to determine x, the weight of cartons that are opened for inspection
The compound inequality statement for the weight of inspected cartons is 630 > X > 690. Here, It can also explain like this:
¶Empty carton weight = 20 oz.
Acceptable weight range per bag of peanuts:
The lower limit is 30.5 oz.
Maximum weight = 33.5 oz
20 bags = 20 peanut bags per carton
Therefore,
The following is the lower limit for carton weight after filling:
630 oz = weight of empty carton + (20 * weight per bag) 20 + (20 * 30.5)
The maximum weight of a carton after it has been filled will be:
Empty carton weight + (20 * weight per bag) 20 + (20 * 33.5) = 690 oz
As a result, the compound inequality for the inspected cartons is: 630 > X > 690.
A peanut company ships its product in a carton that weighs 20 oz when empty. Twenty bags of peanuts are shipped in each carton. The acceptable weight for one bag of peanuts is between 30.5 oz and 33.5 oz, inclusive. If a carton weighs too much or too little, it is opened for inspection. Write and solve a compound inequality to determine x, the weight of cartons that are opened for inspection
The compound inequality statement for the weight of inspected cartons is 630 > X > 690. Here, It can also explain like this:
¶Empty carton weight = 20 oz.
Acceptable weight range per bag of peanuts:
The lower limit is 30.5 oz.
Maximum weight = 33.5 oz
20 bags = 20 peanut bags per carton
Therefore,
The following is the lower limit for carton weight after filling:
630 oz = weight of empty carton + (20 * weight per bag) 20 + (20 * 30.5)
The maximum weight of a carton after it has been filled will be:
Empty carton weight + (20 * weight per bag) 20 + (20 * 33.5) = 690 oz
As a result, the compound inequality for the inspected cartons is: 630 > X > 690.
Fatima plans to spend at least $15 and at most $ 20 on sketch pads and pencils. If she buys 2 sketch pads, how many pencils can she buy while staying in her price range?
Inequalities define the relationship between two non-equal values. Inequality means not being equal. In mathematics, there are five inequality symbols: greater than symbol (>), less than symbol (<), greater than or equal to a sign (≥), less than or equal to a symbol (≤), and not equivalent to a symbol (≠). Many can solve simple inequalities in math by multiplying, dividing, adding, or subtracting both sides until left with the variable.
The compound inequality in this question is solved with the following instructions:
• Let us suppose Fatima purchased 'n' pens.
• Calculating the total money spent on the pens.
• Then solve the inequality by subtraction and division on all sides.
• As a result, you get the answer to how much Fatima spends on pencils while staying within her price range.
Fatima plans to spend at least $15 and at most $ 20 on sketch pads and pencils. If she buys 2 sketch pads, how many pencils can she buy while staying in her price range?
Inequalities define the relationship between two non-equal values. Inequality means not being equal. In mathematics, there are five inequality symbols: greater than symbol (>), less than symbol (<), greater than or equal to a sign (≥), less than or equal to a symbol (≤), and not equivalent to a symbol (≠). Many can solve simple inequalities in math by multiplying, dividing, adding, or subtracting both sides until left with the variable.
The compound inequality in this question is solved with the following instructions:
• Let us suppose Fatima purchased 'n' pens.
• Calculating the total money spent on the pens.
• Then solve the inequality by subtraction and division on all sides.
• As a result, you get the answer to how much Fatima spends on pencils while staying within her price range.
Find the antonym of the underlined word After the car accident ,his memories were quite nebulous.
Find the antonym of the underlined word After the car accident ,his memories were quite nebulous.
What is the meaning of the prefix-sub
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Write a compound inequality to represent the sentence below:
A Quantity x is either less than 10 or greater than 20.
An inequality with a linear function included is referred to as a linear inequality. When the word "and" connects two inequalities, the solution takes place when both inequalities hold true at the same moment. The solution, however, only applies when one of the two inequalities is true when the two are connected by the word "or." The combination or union of the two separate solutions is the solution. When two simple inequalities are combined using either "AND" or "OR," the result is a compound inequality.
One of the two claims is proven to be true by the compound inequality with "AND." If the answers to the separate statements of the compound inequality overlap. While "Or" means that the entire compound sentence is true as long as either of the two statements is true. The solution sets for the various statements are united to form this concept.
Write a compound inequality to represent the sentence below:
A Quantity x is either less than 10 or greater than 20.
An inequality with a linear function included is referred to as a linear inequality. When the word "and" connects two inequalities, the solution takes place when both inequalities hold true at the same moment. The solution, however, only applies when one of the two inequalities is true when the two are connected by the word "or." The combination or union of the two separate solutions is the solution. When two simple inequalities are combined using either "AND" or "OR," the result is a compound inequality.
One of the two claims is proven to be true by the compound inequality with "AND." If the answers to the separate statements of the compound inequality overlap. While "Or" means that the entire compound sentence is true as long as either of the two statements is true. The solution sets for the various statements are united to form this concept.
