Asked by zach
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 =
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 =
Answers
Answered by
zach
Consider the equation: 3(–4n – 9) = 21
Use the distributive property and properties of equality to solve for n.
n =
Use the distributive property and properties of equality to solve for n.
n =
Answered by
zach
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
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
Answered by
zach
incorrect
Answered by
zach
the correct awnser is the addition property of equality and then the division property of equality
Answered by
zach
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.
–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.
Answered by
zach
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?
Which expression represents the amount of money James makes each month?
Which equation represents the scenario?
Answered by
zach
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 =
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 =
Answered by
zach
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
–6(2 + a) = –48
What is the value of a?
a = –6
a = –3
a = 5
a = 6
Answered by
zach
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
.
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
.
Answered by
zach
all of those awnsrs are incorrect
Answered by
zach
Generate a plan and describe the steps needed to solve the equation.
34 = –(m + 3)
Answered by
zach
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
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
Answered by
zach
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
Negative 5 (a + 3) = negative 55
What is the value of a?
Negative 14
Negative 8
8
14
Answered by
zach
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.
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.
Answered by
zach
What is the value of x in the equation below?
6 (x minus 8) = 72
12
15
20
24
6 (x minus 8) = 72
12
15
20
24
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