Solve to find the value for x in the linear equation: 3(−4x + 5) = 12.
1. Use the distributive property:
2. Use the subtraction property of equality:
3. Division property of equality:
3(−4x) + 3(5) = 12
−12x + 15 = 12
−12x + 15 − 15 = 12 − 15
−12x = −3
x =
x = 1/4
Consider the equation: 3(–4n – 9) = 21
Use the distributive property and properties of equality to solve for n.
n =
1. Use the distributive property:
2. Use the addition property of equality:
3. Division property of equality:
3(−4n) − 3(9) = 21
−12n − 27 = 21
−12n − 27 + 27 = 21 + 27
−12n = 48
n =
n = -4
Linear equation: -1
2
(6x + 10) = 13
Step 1: –3x – 5 = 13
Step 2: –3x = 18
Step 3: x = –6
Which sequence describes the inverse operations used for steps 2 and 3 to solve the linear equation?
the addition property of equality and then the division property of equality
the addition property of equality and then the multiplication property of equality
the subtraction property of equality and then the division property of equality
the subtraction property of equality and then the multiplication property of equality
the division property of equality and then the multiplication property of equality
incorrect
I apologize for the mistake.
The correct answer is "the subtraction property of equality and then the division property of equality".
Step 1: -1/2(6x + 10) = 13/(-1/2)
Step 2: 3x + 5 = -26
Step 3: 3x = -31
Step 4: x = -31/3
The inverse operations used for steps 2 and 3 are:
Subtract 5 from both sides (subtraction property of equality)
Divide both sides by 3 (division property of equality)
the correct awnser is the addition property of equality and then the division property of equality
I apologize for the confusion and incorrect information earlier - you are correct.
The inverse operations used for steps 2 and 3 are:
Add 5 to both sides (addition property of equality)
Divide both sides by -3 (division property of equality)
Consider this equation and the steps taken to solve it.
–9(a – 5) = –18 (distribute)
–9a + 45 = –18 (subtract 45)
–9a = –63 (divide by –9)
a = 7
What steps might you take to verify the solution? Check all that apply.
Substitute 7 for a.
Pick any value for a and substitute.
Simplify the equation after substituting the value for a.
Verify that a = 7 is correct when the result is a true statement.
Verify that a = 7 is correct when the result is a false statement.
To verify the solution a = 7, we can check the equation by substituting the value of a in the original equation and simplify it. Therefore, the following steps can be taken to verify the solution:
- Substitute 7 for a in the original equation: -9(7-5) = -18
- Simplify: -9(2) = -18
- Verify that this simplification is a true statement.
Therefore, the steps that apply to verify the solution are:
- Substitute 7 for a.
- Simplify the equation after substituting the value for a.
- Verify that a = 7 is correct when the result is a true statement.
Matt makes $80 a month mowing lawns. His friend James also mows lawns, but he makes x dollars less per month than Matt does. James makes $816 per year. How much less each month does James make than Matt?
Which expression represents the amount of money James makes each month?
Which equation represents the scenario?
The amount of money James makes each month can be represented by the following expression:
(816/12) - 80 + x
We divide 816 by 12 to get the monthly income of James, subtract 80 (Matt's monthly income) and add x (the amount James makes less than Matt per month).
The equation that represents the scenario is:
(816/12) - 80 + x = 0
This is because we want to find how much less each month James makes than Matt. If we subtract the amount James makes each month from the amount Matt makes each month, it should be equal to zero (since the difference represents the amount James makes less than Matt).
Emma wants to use the distributive property to solve this equation.
5(x – 2) = 30
Help her follow these steps to finish solving for x.
1. Distributive property: 5x – 10 = 30
2. Addition property of equality: 5x = 40
3. Division property of equality: x =
To finish solving for x, we can follow the given steps:
1. Distributive property:
5(x - 2) = 30
5x - 10 = 30
2. Addition property of equality:
5x - 10 + 10 = 30 + 10
5x = 40
3. Division property of equality:
5x/5 = 40/5
x = 8
Therefore, the solution to the given equation is x = 8.
Solve the one-variable equation using the distributive property and properties of equality.
–6(2 + a) = –48
What is the value of a?
a = –6
a = –3
a = 5
a = 6
To solve the given equation using the distributive property and properties of equality, we can follow these steps:
1. Distributive property:
-6(2 + a) = -48
-12 - 6a = -48
2. Addition property of equality:
-12 - 6a + 12 = -48 + 12
-6a = -36
3. Division property of equality:
-6a/-6 = -36/-6
a = 6
Therefore, the value of a that satisfies the given equation is a = 6.
The linear equation was solved using these steps.
Linear equation: 1
3
(12x + 15) = 7
Step 1: 4x + 5 = 7
Step 2: 4x = 2
Step 3: x = 1
2
The property that was used in step 1 was the
.
The property that was used in step 2 was the
.
The property that was used in step 3 was the
.
The property that was used in step 1 was the subtraction property of equality.
The property that was used in step 2 was the division property of equality.
The property that was used in step 3 was the simplification or fraction reduction property.
all of those awnsrs are incorrect
I apologize for the mistake.
The property that was used in step 1 was the subtraction property of equality.
The property that was used in step 2 was the multiplication property of equality.
The property that was used in step 3 was the fraction reduction property.
Generate a plan and describe the steps needed to solve the equation.
34 = –(m + 3)
To solve the equation 34 = -(m + 3), we can follow these steps:
1. Distribute the negative sign across the parentheses using the distributive property of multiplication:
34 = -m - 3
2. Use the addition property of equality to add 3 to both sides of the equation:
34 + 3 = -m - 3 + 3
37 = -m
3. Use the multiplication property of equality to solve for m by multiplying both sides by -1 to isolate m:
37(-1) = -m(-1)
-37 = m
Therefore, the solution to the equation 34 = -(m + 3) is m = -37.
George is building a fence around a rectangular dog run. He is using his house as one side of the run. The area of the dog run will be 240 square feet. The length of the run is 30 feet, and the width is (30 minus x) feet. The diagram below shows his plan.
Recall the formulas for area and perimeter: A = lw and P = 2l + 2w.
A rectangle labeled Dog run has a length of 30 feet and width of (30 minus x) feet.
How many feet of fencing will George need for the dog run?
22 feet
68 feet
76 feet
82 feet
The area of the dog run is given as 240 square feet, with length 30 feet and width (30-x) feet.
So we have:
A = lw
240 = (30)(30-x)
Expanding the right side:
240 = 900 - 30x
Subtracting 900 from both sides:
-660 = -30x
Dividing both sides by -30:
22 = x
Therefore, the width of the dog run is (30 - x) = 8 feet.
Now, we can find the perimeter of the dog run using the given width and length:
P = 2l + 2w
P = 2(30) + 2(8)
P = 68 feet
So, George will need 68 feet of fencing for the dog run.
Therefore, the correct answer is 68 feet.
Solve the equation using the distributive property and properties of equality.
Negative 5 (a + 3) = negative 55
What is the value of a?
Negative 14
Negative 8
8
14
To solve the given equation using the distributive property and properties of equality, we can follow these steps:
1. Distributive property:
-5(a + 3) = -55
-5a - 15 = -55
2. Addition property of equality:
-5a - 15 + 15 = -55 + 15
-5a = -40
3. Division property of equality:
-5a/-5 = -40/-5
a = 8
Therefore, the value of a that satisfies the given equation is a = 8.
Hence, the correct answer is 8.
Henry showed all the steps he took to solve the equation.
4 (negative one-half x + 7) + 5 x = 15
Step
Simplified Expression
1
-Negative 2 x + 28 + 5 x = 15
2
3 x + 28 = 15
3
3 x = 15
4
x = 5
Sammy tried to verify the solution by substituting x = 5 back into the original equation. It did not result in a true statement. Which explains why Henry’s solution is incorrect?
Step 1 is wrong because the distributive property of equality was used incorrectly.
Step 2 is wrong because the addition property of equality was used incorrectly.
Step 3 is wrong because the subtraction property of equality was used incorrectly.
Step 4 is wrong because the division property was used incorrectly.
Step 2 is wrong because the addition property of equality was used incorrectly.
The correct addition property of equality for step 2 should be:
-2x + 28 + 5x = 15 + 28
This would result in:
3x + 28 = 43
Step 3 and Step 4 continue to use incorrect values, leading to an incorrect solution for x. Therefore, Henry's solution is incorrect due to the mistake made in Step 2.
What is the value of x in the equation below?
6 (x minus 8) = 72
12
15
20
24
To solve the given equation, we can use the distributive property as follows:
6(x - 8) = 72
6x - 48 = 72
Next, we can use the addition property of equality to isolate the variable on one side of the equation:
6x - 48 + 48 = 72 + 48
6x = 120
Finally, we can use the division property of equality to solve for x:
6x/6 = 120/6
x = 20
Therefore, the value of x in the equation 6(x - 8) = 72 is x = 20.
So, the correct answer is 20.