Maria solved the equation.
4 (3 x minus 8) minus 4 = 24. 12 x minus 32 minus 4 = 24. 12 x minus 36 = 24. 12 x = 60. x = 5.
What methods did she use and in what order did she use them?
combining like terms
distributive property
addition property of equality
division property of equality
distributive property
addition property of equality
subtraction property of equality
division property of equality
distributive property
combining like terms
addition property of equality
division property of equality
distributive property of equality
addition property of equality
combining like terms
division property of equality
The methods Maria used and the order in which she used them are:
1. Distributive property: 4(3x - 8) = 12x - 32
2. Combining like terms: 12x - 32 - 4 = 12x - 36
3. Subtraction property of equality: 12x - 36 = 24
4. Addition property of equality: 12x = 60
5. Division property of equality: x = 5
be more specific please
Sure, I apologize for the previous response not being specific enough. Here is a more detailed explanation of the methods Maria used and the order in which she used them:
1. Distributive property: Maria applied the distributive property to simplify the expression on the left side of the equation. The expression 4(3x - 8) can be expanded by multiplying 4 to both terms inside the parentheses, resulting in 12x - 32.
2. Combining like terms: Maria combined the constant terms on the left side of the equation by subtracting 4 from 12x - 32, resulting in 12x - 36.
3. Subtraction property of equality: Maria applied the subtraction property of equality to subtract 24 from both sides of the equation, resulting in 12x - 36 = 24.
4. Addition property of equality: Maria applied the addition property of equality to add 36 to both sides of the equation, resulting in 12x = 60.
5. Division property of equality: Maria applied the division property of equality by dividing both sides of the equation by 12, resulting in x = 5.
Which method should be used to solve for x?
2.5 x = 5.7
distributive property
addition property of equality
combining like terms
division property of equality
To solve for x in the equation 2.5x = 5.7, the method that should be used is the division property of equality.
Explanation:
The division property of equality states that if we divide both sides of an equation by the same non-zero number, the equation remains true. In this case, we can divide both sides of the equation by 2.5 which is the coefficient of x to isolate x on one side of the equation.
2.5x/2.5 = 5.7/2.5
x = 2.28
Therefore, x equals 2.28, which can be found by applying the division property of equality.
Consider the equation and its solution.
Negative 15 (x minus box) = 25. Negative 15 x + 30 = 25. Negative 15 x = negative 5. x = one-third.
What number should be in the empty box?
Negative 30
Negative 2
2
30
To find what number should be in the empty box in the equation Negative 15 (x - box) = 25, we can follow the steps that were used to solve the equation:
- Distribute the negative 15: Negative 15 x + 15(box) = 25.
- Subtract 15 from both sides: Negative 15x = 25 - 15 box.
- Divide both sides by negative 15: x - box = -5/3.
- Add box to both sides: x = box - 5/3.
Now we can substitute the value of x found in the solution, which is x = 1/3, and solve for box:
1/3 = box - 5/3
Multiplying both sides by 3:
1 = 3box - 5
Adding 5 to both sides:
6 = 3box
Dividing both sides by 3:
2 = box
Therefore, the number that should be in the empty box is 2.
Which step shows the result of applying the subtraction property of equality?
One-fourth (12 x + 8) + 4 = 3
Step
Solution
1
3 x + 2 + 4 = 3
2
3 x + 6 = 3
3
3 x = negative 3
4
x = negative 1
Step 1
Step 2
Step 3
Step 4
The step that shows the result of applying the subtraction property of equality is Step 2.
Explanation:
To solve the equation One-fourth (12x + 8) + 4 = 3, the first step is to simplify the expression on the left side of the equation by applying the distributive property of multiplication over addition. This gives:
3x + 2 + 4 = 3
The next step is to combine like terms on the left side of the equation, which gives:
3x + 6 = 3
At this point, we can see that the left side of the equation can be simplified further by applying the subtraction property of equality, which states that if we subtract the same quantity from both sides of an equation, the equation remains true. In this case, we can subtract 6 from both sides of the equation to isolate the variable term on one side of the equation and the constant term on the other side, which gives:
3x = -3
Therefore, Step 2 shows the result of applying the subtraction property of equality.
Consider the solution to the linear equation.
5 (x + 6) = 50. 5 x + 30 = 50. 5 x = 20. x = 4.
Which describes the inverse operations used after the distributive property?
addition then division
subtraction then division
multiplication then subtraction
division then addition
The inverse operations used after the distributive property in the solution are subtraction and then division.
Explanation:
After applying the distributive property to simplify the expression in the equation:
5(x + 6) = 50
we get:
5x + 30 = 50
To solve for x, we want to isolate x on one side of the equation and determine its value. To do this, we can use inverse operations in the reverse order of operations applied to the equation.
First, we can apply the inverse operation of addition by subtracting 30 from both sides of the equation to isolate 5x on one side:
5x = 20
At this point, we want to solve for x by isolating it on one side of the equation. The inverse operation that has been applied to 5x is multiplication, so we use the inverse operation of multiplication, which is division, to isolate x:
x = 4
Therefore, the inverse operations used in the solution after the distributive property are subtraction then division.
What property was used in step 1 to arrive at step 2?
Step 1: 5 (x minus 7) = 55. Step 2: 5 x minus 35 = 55. Step 3: 5 x = 90. Step 4: x = 18.
distributive property
addition property of equality
subtraction property of equality
division property of equality
The property used in Step 1 to arrive at Step 2 is the distributive property.
Explanation:
In Step 1, we are given the equation:
5(x - 7) = 55
To solve for x, we need to simplify the expression on the left side of the equation by distributing the 5. So, we use the distributive property which states that:
a(b + c) = ab + ac
To distribute 5 to the terms inside the parentheses, we have:
5(x - 7) = 5x - 35
So, Step 1 is using the distributive property to simplify the expression on the left side of the equation by multiplying 5 to both terms inside the parentheses.
Therefore, the property used in Step 1 to arrive at Step 2 is the distributive property.
Solve this linear equation for p.
2.6(5.5p – 12.4) = 127.92
1. Distributive property: 14.3p − 32.24 = 127.92
2. Addition property of equality: 14.3p − 32.24 + 32.24 = 127.92 + 32.24
14.3p = 160.16
3. Division property of equality:
14.3p
14.3
=
160.16
14.3
4. Solution: p =
11.2
Big Time Movers charges an initial fee of $24.50, plus $12.75 an hour for their moving services. On holidays, they charge 2.5 times their regular total amount. If they made $188.75 on a job on New Year’s Day, how many hours did they work?
This equation represents the data:
2.5(12.75x + 24.50) = 188.75
Big Time Movers worked
hours on New Year’s Day.
To find the number of hours Big Time Movers worked on New Year’s Day, we need to solve the equation 2.5(12.75x + 24.50) = 188.75 where x represents the number of hours worked.
Here are the steps to solve the equation:
1. Distribute 2.5 to the terms inside the parentheses:
31.875x + 61.25 = 188.75
2. Subtract 61.25 from both sides:
31.875x = 127.50
3. Divide both sides by 31.875:
x = 4
Therefore, Big Time Movers worked 4 hours on New Year's Day.
Jerome solved the equation 1
3
x + 5
6
= 1 as shown.
1. Subtraction property
of equality: 1
3
x + 5
6
− 5
6
= 1
1
− 5
6
2. LCD: 1
3
x = 1
6
− 5
6
3. Multiply by the
reciprocal: ( 3
1
) 1
3
x = −4
6
( 3
1
)
4. Solve and simplify: x = −12
6
= −2
Analyze Jerome’s steps. In which step did he make an error?
In step 1, he needed to add StartFraction 5 Over 6 EndFraction to both sides of the equation.
In step 2, the LCD was not used correctly to make equivalent fractions.
In step 3, the correct reciprocal was not multiplied to both sides.
In step 4, the answer was not reduced correctly.
Jerome did not make an error in any of his steps.
Explanation:
Step 1 is correct, as Jerome used the subtraction property of equality to subtract 5/6 from both sides of the equation to isolate the x-term.
Step 2 is also correct, as Jerome found the least common denominator (LCD) of 3 and 6 to be 6, and used it to write equivalent fractions for both sides of the equation.
Step 3 is correct as well, as Jerome multiplied both sides of the equation by the reciprocal of 1/3 to isolate x.
Step 4 is also correct, as Jerome simplified the answer by dividing both the numerator and denominator of -12/6 by the greatest common factor of 12 and 6, which is 6, to get -2.
Therefore, Jerome did not make an error in any of his steps.
your awnser is very incorrect
I apologize for the incorrect answer. I will provide a corrected response below:
The error in Jerome's steps is in Step 2.
Explanation:
In Step 2, Jerome converted the fractions on both sides of the equation to have a common denominator of 6. However, he did not multiply the numerator of 1/3 x by 2 when he multiplied the denominator by 2. This resulted in the equation being incorrect.
To correct the error, we need to multiply 1/3 x by 2/2, which gives us 2/6 x. Then, we can rewrite Step 2 using a common denominator of 6 as follows:
2/6 x + 5/6 = 1/6
Subtracting 5/6 from both sides of the equation, we have:
2/6 x = - 4/6
Simplifying by dividing both sides by 2/6, we get:
x = -2
Therefore, the corrected answer is that the error in Jerome's steps is in Step 2.