Match the equation with its solution.
3i+2i−4=18i
3(2i−7)=6i−21
2i+3=2i−5
1) 3i+2i−4=18i - No solution
2) 3(2i−7)=6i−21 - i = −6
3) 2i+3=2i−5 - No solution
Match the equation with its solution.
3i+2i−4=18i
3(2i−7)=6i−21
2i+3=2i−5
1) 3i+2i−4=18i - No solution
2) 3(2i−7)=6i−21 - i = −6
3) 2i+3=2i−5 - No solution
Which equation has the SAME FIRST STEP to solve as this equation: 2x+12−3x=27?
(1 point)
Responses
4x−17+2x=9
4 x minus 17 plus 2 x is equal to 9
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
The equation that has the same first step to solve as 2x+12−3x=27 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=24−20x
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+10=−24+20x
35 x plus 10 is equal to negative 24 plus 20 x
5x+14=6+20x
5 x plus 14 is equal to 6 plus 20 x
35x+2=−24−5x
Using the Distributive Property, the equation 7(5x+2)=−4(6−5x) simplifies to 35x+14=−24+20x.
For the equation 2(x−5)=9−3x+6+8+3x+7
, the left side of the equation can be simplified by using the Distributive Property, and the right side of the equation can be simplified by combining like terms.
Simplify the left side of the equation:
Simplify the right side of the equation:
Simplifying the left side of the equation using the Distributive Property:
2(x-5) = 2 * x + 2 * (-5) = 2x - 10
Simplifying the right side of the equation by combining like terms:
9 - 3x + 6 + 8 + 3x + 7 = (9 + 6 + 8 + 7) + (-3x + 3x) = 30 + 0 = 30
So the simplified equation is:
2x - 10 = 30
2(x−5)=9−3x+6+8+3x+7
Simplify the left side of the equation:
Simplifying the left side of the equation:
2(x-5) = 2x - 10
now Simplify the right side of the equation
Simplifying the right side of the equation:
9 - 3x + 6 + 8 + 3x + 7 can be combined as follows:
= (9 + 6 + 8 + 7) + (-3x + 3x)
= 30 + 0
= 30
So the simplified equation is:
2x - 10 = 30
Jill solves the equation 3(x−5)+2x=0
. Fill in the blanks with the correct values:
3x+
Response area +2x=0
5x=
Response area
x=
Response area
Jill solves the equation 3(x−5)+2x=0. Fill in the blanks with the correct values:
3x + (-15) + 2x = 0
5x - 15 = 0
x = 3
Solve the equation by filling in the steps: 2(x−3)+21=−3
(4 points)
Step 1: Distribute to get
Step 2: Combine like terms to get
Step 3: Use
to get 2x=−18
Step 4: Use
to get x=−9
Solve the equation by filling in the steps: 2(x−3)+21=−3
Step 1: Distribute to get 2x - 6 + 21 = -3
Step 2: Combine like terms to get 2x + 15 = -3
Step 3: Use subtraction to isolate the variable: 2x = -18
Step 4: Use division to solve for x: x = -9
After combining like terms to simplify the equation 3−15x+24+16x=4x−24−4x
, what would be the next best step to finish solving?(1 point)
Responses
Subtract x from both sides of the equation.
Subtract x from both sides of the equation.
Divide both sides of the equation by 15.
Divide both sides of the equation by 15.
Add 24 to both sides of the equation.
Add 24 to both sides of the equation.
Subtract 24 from both sides of the equation.
Subtract 24 from both sides of the equation.
Add x to both sides of the equation.
Add x to both sides of the equation.
Subtract 27 from both sides of the equation.
The next best step to finish solving the equation 3−15x+24+16x=4x−24−4x is to subtract 24 from both sides of the equation.
4(2−3x)=x−2(2x+1)
8−3x=x−4x−2
8−3x=−3x−2
No solution
The correct simplification after combining like terms would be:
8 - 3x = x - 4x - 2
Then, we simplify further:
8 - 3x = -3x - 2
This equation has no solution.
4(2−3x)=x−2(2x+1)
8−3x=x−4x−2
8−3x=−3x−2
No solution
is this true
Apologies for the confusion in my previous response. The statements you provided are not correct.
Let's solve the equation step by step:
1) Distribute the 4 on the left side and the -2 on the right side:
8 - 12x = x - 4x - 2
2) Combine like terms:
8 - 12x = -3x - 2
3) Add 12x to both sides of the equation:
8 = 9x - 2
4) Add 2 to both sides of the equation:
10 = 9x
5) Divide both sides by 9:
x = 10/9
So, the true solution to the equation is x = 10/9.
The speed limit sign on the expressway says that the speed limit is 55 mph. Write an equality that represents all speeds you can legally drive on the expressway.(1 point)
Responses
x≥55
x is greater than or equal to 55
x<55
x<55
x≤55
x is less than or equal to 55
x>55
The correct equality that represents all speeds you can legally drive on the expressway is:
x ≤ 55