Five less than three-fourths of x is seven. If x equals 16, what is the last property of equality you would use to justify the solution to this problem?(1 point
The last property of equality that would be used to justify the solution to this problem is the Subtraction Property of Equality.
Andrea is 6 years younger than Tony. In two years, Tony will be three times as old as Andrea. Let a be Tony’s current age. Which of these linear equations can be used to find Andrea’s and Tony’s current ages?
The linear equation that can be used to find Andrea's and Tony's current ages is:
a - 6 = 2(t + 2), where a is Tony's current age and t is Andrea's current age.
Andrea is 6 years younger than Tony. In two years, Tony will be three times as old as Andrea. Let a be Tony’s current age. Which of these linear equations can be used to find Andrea’s and Tony’s current ages?(1 point)
Responses
a+2=3(a+6+2)
a=3(a+2)
3(a+2)=a−6+2
a+2=3(a−6+2)
Andrea is 6 years younger than Tony. In two years, Tony will be three times as old as Andrea. Let a be Tony’s current age. Which of these linear equations can be used to find Andrea’s and Tony’s current ages?(1 point)
A. a+2=3(a+6+2)
B. a=3(a+2)
C. 3(a+2)=a−6+2
D. a+2=3(a−6+2)
The correct linear equation that can be used to find Andrea's and Tony's current ages is:
D. a+2=3(a−6+2)
A string is cut in two so that one section is 5 inches longer than the other. Twice the length of the longer section is three times the length of the shorter section. Write an equation that allows you to solve for the length of the shorter section. How long is the shorter section?(1 point)
A.15 inches
B. 20 inches
C. 12 inches
D. 10 inches
Let's assume that the length of the shorter section is x inches. According to the problem, the longer section is 5 inches longer, so its length is x + 5 inches.
We are also given that twice the length of the longer section is three times the length of the shorter section. This can be expressed as:
2(x + 5) = 3x
Simplifying the equation, we get:
2x + 10 = 3x
10 = 3x - 2x
10 = x
Therefore, the length of the shorter section is 10 inches, which corresponds to option D.
Manipulate the equation y=7x−12 so that it is written in terms of x. Which equation is equivalent to y=7x−12?(1 point)
A. x=(y+12)7
B. x=(y12)−7
C. x=(y−12)7
D. x=(y7)+12
To manipulate the equation y=7x−12 so that it is written in terms of x, we need to isolate x.
Adding 12 to both sides of the equation:
y + 12 = 7x
Dividing both sides of the equation by 7:
(x = (y + 12) / 7
So the corresponding equation is:
A. x = (y + 12) / 7