Which equation has the same first step to solve as this equation: 2x+12−3x=27
(1 point)
Responses
2x+12=27
2 x plus 12 is equal to 27
2(x−5)+2x=10
2 times open paren x minus 5 close paren plus 2 x is equal to 10
2x+12=−3x−27
2 x plus 12 is equal to negative 3 x minus 27
4x−17+2x=9
4 x minus 17 plus 2 x is equal to 9
Question 3
The equation that has the same first step to solve as the given equation is:
2x+12=27
Using the Distributive Property as a good first step to solving the equation 7(5x+2)=−4(6−5x)
, you could simplify this equation to get which of these choices?(1 point)
Responses
35x+2=−24−5x
35 x plus 2 is equal to negative 24 minus 5 x
35x+2=24−20x
35 x plus 2 is equal to 24 minus 20 x
35x+14=−24+20x
35 x plus 14 is equal to negative 24 plus 20 x
35x+14=−24−20x
35 x plus 14 is equal to negative 24 minus 20 x
5x+14=6+20x
The simplified equation after using the Distributive Property would be:
35x + 14 = -24 - 20x
13. The speed limit sign on the expressway says that the speed limit is 55 mph. Write an inequality that represents all speeds you can legally drive on the expressway. (1 point)
The inequality that represents all speeds you can legally drive on the expressway is:
v ≤ 55
where v represents the speed in mph.
The equation that has the same first step to solve as the equation 2x+12−3x=27 is 2x+12=27.
To determine which equation has the same first step to solve as the given equation, let's break down the steps of solving the given equation:
1. Combine like terms on both sides of the equation.
2. Move all the x terms to one side of the equation and numerical terms to the other side.
3. Simplify the equation.
4. Solve for x.
Let's apply these steps to each of the provided equations to see which one matches the first step of the given equation (2x + 12 - 3x = 27).
1. Equation: 2x + 12 = 27
Explanation: Combine like terms on both sides by subtracting 3x from 2x.
This equation matches the first step of the given equation: 2x + 12 - 3x = 27, so it is the correct answer.
2. Equation: 2(x − 5) + 2x = 10
Explanation: This equation starts with distributing the 2 to the terms inside the parentheses, which is not the first step of the given equation. So, it is not the correct answer.
3. Equation: 2x + 12 = −3x − 27
Explanation: This equation starts with combining like terms on both sides of the equation, which is not the first step of the given equation. So, it is not the correct answer.
4. Equation: 4x − 17 + 2x = 9
Explanation: This equation starts with combining like terms on the left side by adding 4x to 2x. This is not the first step of the given equation. So, it is not the correct answer.
Therefore, the equation that has the same first step to solve as the given equation (2x + 12 - 3x = 27) is 2x + 12 = 27.