To solve for b in the equation A = 1/2 (a + b), we can start by distributing the 1/2 to both terms in the parentheses:
A = 1/2a + 1/2b
Next, we can isolate b by subtracting 1/2a from both sides of the equation:
A - 1/2a = 1/2b
Using the distributive property on the left side of the equation, we have:
1/2A - 1/4a = b
Therefore, the equation is:
b = 1/2A - 1/4a
Solve for b in the following formula: A = 1/2 (a + b)
b = 1/2 A - a
b = 2 A + a
b = 2 A - a
b = 1/2 A + a
11 answers
bot you have to choose from one of the options
Apologies for the confusion. To solve for b, we need to rearrange the equation A = 1/2 (a + b):
First, multiply both sides by 2 to get rid of the fraction:
2A = a + b
Next, subtract a from both sides to isolate b:
2A - a = b
Therefore, the correct equation to solve for b is:
b = 2A - a.
First, multiply both sides by 2 to get rid of the fraction:
2A = a + b
Next, subtract a from both sides to isolate b:
2A - a = b
Therefore, the correct equation to solve for b is:
b = 2A - a.
A student solves the following problem: Problem: 2(x−3) + 3x = 19
Step 1: 2x − 6 + 3x = 19
Step 2: (2x + 3x) −6 = 19
Step 3: 5x − 6 = 19
Step 4: 5x - 6 + 6 = 19 + 6
Step 5: 5x = 25
Step 6: x = 5
What property justifies going from step 3 to step 4?
Division Property of Equality
Commutative Property of Addition
Substitution Property
Distributive Property
Addition Property of Equality
Step 1: 2x − 6 + 3x = 19
Step 2: (2x + 3x) −6 = 19
Step 3: 5x − 6 = 19
Step 4: 5x - 6 + 6 = 19 + 6
Step 5: 5x = 25
Step 6: x = 5
What property justifies going from step 3 to step 4?
Division Property of Equality
Commutative Property of Addition
Substitution Property
Distributive Property
Addition Property of Equality
The property that justifies going from step 3 to step 4 is the Addition Property of Equality.
A student solved the equation x + 2 (x + 1) = 17 below and showed their work in the table below.
Problem x + 2 (x + 1) = 17
Line 1: x + 2x + 2 = 17
Line 2: 3x + 2 = 17
Line 3: 3x = 15
Line 4: x = 45
Identify the property used to arrive at Line 1.
Identify the property used to arrive at Line 2.
What line has a mistake?
What should have been the correct answer for that line?
Choices:
Combine like terms
Addition property of equality
Division property of equality
Distributive Property
Substitution
Line 2
Line 3
Line 4
x = 15
x = 5
x = 3
Problem x + 2 (x + 1) = 17
Line 1: x + 2x + 2 = 17
Line 2: 3x + 2 = 17
Line 3: 3x = 15
Line 4: x = 45
Identify the property used to arrive at Line 1.
Identify the property used to arrive at Line 2.
What line has a mistake?
What should have been the correct answer for that line?
Choices:
Combine like terms
Addition property of equality
Division property of equality
Distributive Property
Substitution
Line 2
Line 3
Line 4
x = 15
x = 5
x = 3
The property used to arrive at Line 1 is the Distributive Property.
The property used to arrive at Line 2 is the Combining Like Terms property.
Line 4 has a mistake.
The correct answer for Line 4 should be x = 5.
The property used to arrive at Line 2 is the Combining Like Terms property.
Line 4 has a mistake.
The correct answer for Line 4 should be x = 5.
Fill in the blanks to follow the steps in solving the equation: 5x − 12 − 6x = −10x + 7 − 1
Step 1: Combine like terms to get: ?
Step 2: Get the x-terms on the same side of the equation: ?
Step 3: Get the constants on the same side of the equation: ?
Step 4: Use Division Property of Equality: ?
Choices:
−x − 12 = −10x + 6
5x − 18 = −3x − 1
x − 12 = −10x − 6
9x −12 = 6
−12 = −11x + 6
8x − 18 = −1
8x = 19
9x = 18
−18 = −11x
x = 2
x = 0
x = 11/18
Step 1: Combine like terms to get: ?
Step 2: Get the x-terms on the same side of the equation: ?
Step 3: Get the constants on the same side of the equation: ?
Step 4: Use Division Property of Equality: ?
Choices:
−x − 12 = −10x + 6
5x − 18 = −3x − 1
x − 12 = −10x − 6
9x −12 = 6
−12 = −11x + 6
8x − 18 = −1
8x = 19
9x = 18
−18 = −11x
x = 2
x = 0
x = 11/18
Step 1: Combine like terms to get: -x - 12 = -10x + 6
Step 2: Get the x-terms on the same side of the equation: -x + 10x - 12 = 6
Step 3: Get the constants on the same side of the equation: 9x - 12 = 6
Step 4: Use Division Property of Equality: 9x = 18
Therefore, the correct statements for each step are:
Step 1: -x - 12 = -10x + 6
Step 2: -x + 10x - 12 = 6
Step 3: 9x - 12 = 6
Step 4: 9x = 18
Hence, the correct answer is 9x = 18.
Step 2: Get the x-terms on the same side of the equation: -x + 10x - 12 = 6
Step 3: Get the constants on the same side of the equation: 9x - 12 = 6
Step 4: Use Division Property of Equality: 9x = 18
Therefore, the correct statements for each step are:
Step 1: -x - 12 = -10x + 6
Step 2: -x + 10x - 12 = 6
Step 3: 9x - 12 = 6
Step 4: 9x = 18
Hence, the correct answer is 9x = 18.
bot what's step two, i don't see that option
Apologies for the confusion. The step two should be:
Step 2: Get the x-terms on the same side of the equation: 5x - 6x - 12 = -10x + 7 - 1
Therefore, the correct statement for step 2 is: 5x - 6x - 12 = -10x + 7 - 1.
Step 2: Get the x-terms on the same side of the equation: 5x - 6x - 12 = -10x + 7 - 1
Therefore, the correct statement for step 2 is: 5x - 6x - 12 = -10x + 7 - 1.