Which equation has the same solution for x as this equation: x−12=40
?(1 point)
Responses
x2=14
x4=13
x+12=−40
12−x=40
x+12=-40
. The length of a rectangle is four meters less than twice its width.
If the area of the rectangle is 96 m^2, what is the length and the width?
(3 points)
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An expression for the length of the rectangle in terms of the width would be Response area
The formula for the area of a rectangle is Response area
Using trial and error, if the area is 96 m^2, then the length and width are Response area
An expression for the length of the rectangle in terms of the width would be 2w - 4.
The formula for the area of a rectangle is length * width.
Using trial and error, if the area is 96 m^2, then the length and width are 12 m and 8 m respectively.
Match the equation with its solution(s).(5 points)
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3(2i−7)=15
3i+2i−7=18
3i+5=3i+7
3(2i+7)=6i+21
3i+5=2i−7
3(2i−7)=15 - Solution: i = 6
3i+2i−7=18 - Solution: i = 5
3i+5=3i+7 - No solution
3(2i+7)=6i+21 - Solution: i = -1
3i+5=2i−7 - Solution: i = -12
Solve the equation justifying each step with the correct reasoning.
2(x+8)=2x+8
(5 points)
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Step 1: Response area Property to get Response area simplified equation
Step 2: Response area Property to get Response area simplified equation
For this equation, there is/are Response area
Step 1: Distribute the 2 to both terms inside the parentheses.
2(x+8) = 2x + 2(8)
Step 2: Simplify the right side of the equation.
2(x+8) = 2x + 16
For this equation, there is no further simplification or solving required. The simplification in Step 2 is the final solution.
Match the description of the one variable equation with the number of solutions it will have.(4 points)
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x−7=7−x
3(x+5)=3x+5
10−x=25
2(x+4)=2x+5+3
x−7=7−x - One solution
3(x+5)=3x+5 - Infinite solutions
10−x=25 - No solution
2(x+4)=2x+5+3 - No solution
A student wants to purchase some new school supplies. He wants to buy a calculator that costs $24 and some notebooks for school. Each notebook costs $2. The student only has $37 to spend.
Let n represent the number of notebooks that he buys.
Which inequality describes this scenario?
(1 point)
Responses
37≥2n+24
37<2n+24
37>2n+24
24n+2≥37