Which property should Remus use to solve the equation below?
7 q = 49
Which property should Remus use to solve the equation below?
7 q = 49
Remus should use the division property of equality to solve the equation.
The sum of Micah’s age and Aria’s age is 29. Aria is 5 years older than twice Micah’s age. Let x represent Micah’s age. The equation that can be used to find Micah’s age is
x + (2x + 5) = 29
Kamal solved an equation as shown below.
3 (x minus 8) = x + 2 x + 7. 3 x minus 24 = 3 x + 7. negative 24 = 7.
What is the solution to Kamal’s equation?
Kamal's work doesn't provide a valid solution.
In Kamal's work, the equation 3(x-8)=x+2x+7 is first simplified to 3x-24=3x+7. This step is incorrect - distributing the 3 on the left side gives 3x-24, but distributing on the right side should give 3x+6, not 2x+7.
If we simplify the original equation properly, we get:
3(x-8) = x+2x+7
3x - 24 = 3x + 7 (distribute 3 on left and combine like terms on right)
-24 = 7 (subtract 3x from both sides)
No solution can be found since -24 ≠ 7.
What is the value of x when solving the equation Negative 2 x + (negative 8) = 2 x + 8 using algebra tiles?
To solve the equation using algebra tiles, we need to balance both sides of the equation using zero pairs.
Start by representing -2x with two red tiles, and -8 with eight yellow tiles. Then represent 2x with two green tiles, and 8 with eight blue tiles.
[Image of the tiles: |RR| + |RRRRRRRR| + |YYYYYYYY| = |GG| + |GG| + |BBBBBBBB| + |BBBBBBBB|]
We want to move some tiles around so that the red and green tiles end up on the same side. We can do this by moving two green tiles to the left side, and two red tiles to the right side. This is equivalent to adding 2x to both sides of the equation.
[Image of the tiles after moving them: |RRRRRRRR| + |YYYYYYYY| + |GG| + |GG| = |RR| + |BB| + |BB| + |BBBBBBBB|]
Now we can see that we have zero pairs of red and green tiles: the two red tiles on the right side can be paired with two green tiles on the left side. We can also see that we have zero pairs of yellow and blue tiles. This means that the equation is balanced.
Since we started with -2x on the left side and ended with 4x on the left side (the two green tiles represent 2x each), we know that 4x = -8, or x = -2.
Therefore, the value of x is -2.
Juanita wants to model the equation 3 x + 2 = negative x + 6. She begins with the tiles below.
3 x tiles and 2 positive 1 tiles = 1 negative x tile
How can Juanita complete her model?
First, we need to rearrange the equation so that all the x terms are on one side and the constant terms are on the other side:
3x + 2 = -x + 6
Add x to both sides:
4x + 2 = 6
Subtract 2 from both sides:
4x = 4
Divide by 4:
x = 1
Now we can use this value of x to complete the model. Start with the 3x tiles and 2 positive 1 tiles that Juanita has already placed.
[Image of the tiles: |XXX| + |1| + |1| = |NX| ]
We know that x = 1, so we represent this with one green tile. We also know that -x = -1, so we represent this with one red tile.
[Image of the tiles after adding the green and red tiles: |XXX| + |1| + |1| + |G| = |NX| + |R|]
Now we can see that we have zero pairs of x and -x tiles (the green and red tiles can be paired), so we can simplify the model:
[Image of the simplified tiles: |XX| + |1| + |1| = ]
This shows that the model is balanced and x = 1 is a valid solution to the equation.
choose a awnser fior the previous question Put 4 yellow unit tiles on the left side of the equal sign.
Put 4 yellow unit tiles on the right side of the equal sign.
Put 6 green x-tiles on the right side of the equal sign.
Put 6 yellow unit tiles on the right side of the equal sign.
None of the answer choices is correct.
In the given equation 3x + 2 = -x + 6, we need to create models for both sides of the equation using algebra tiles and then balance them by moving the tiles around.
Starting with the left side:
The 3x term can be represented with 3 green x-tiles. The positive 2 can be represented with 2 yellow unit tiles. So, after initial modeling, the left side looks like:
[Image of the tiles on the left side: |XXX| + |Y| + |Y|]
Now, let's work on the right side:
The -x term can be represented with 1 red x-tile. The positive 6 can be represented with 6 yellow unit tiles. So, after initial modeling, the right side looks like:
[Image of the tiles on the right side: |RX| + |YYYYYY|]
Now, let's balance the equation:
The left side currently has 3 green x-tiles and 2 yellow unit tiles, so we need to add 1 red x-tile and 4 yellow unit tiles to the left side. We can also move 2 yellow unit tiles from the left side to the right side to balance out the yellow tiles. So, the balanced equation looks like:
[Image of the balanced tiles: |XXX| + |Y| + |Y| + |RX| + |YY| + |YY| + |YY|]
This shows that the solution to the equation is x = 1.
thats incorrect
I apologize for the confusion. Can you please clarify which question you are referring to and what the correct answer is? I'm here to help you, and I want to make sure that I provide you with accurate information.
Juanita wants to model the equation 3 x + 2 = negative x + 6. She begins with the tiles below.
3 x tiles and 2 positive 1 tiles = 1 negative x tile
How can Juanita complete her model?
Put 4 yellow unit tiles on the left side of the equal sign.
Put 4 yellow unit tiles on the right side of the equal sign.
Put 6 green x-tiles on the right side of the equal sign.
Put 6 yellow unit tiles on the right side of the equal sign.
Juanita can complete her model as shown below:
- Start with the given tiles: 3 x tiles and 2 positive 1 tiles on the left side of the equal sign and 1 negative x tile on the right side of the equal sign.
[Image of the tiles: |XXX| + |1| + |1| = |NX| ]
- To balance the equation, we want to move the x terms to the left side and the constant terms to the right side. So, we need to add 1 x-tile to the left side and 6 unit tiles to the right side.
[Image of the tiles after balancing: |XXX| + |1| + |1| + |X| = |NX| + |U| + |U| + |U| + |U| + |U| + |U|]
- Now we can see that we have zero pairs of x and -x tiles (the green and red tiles can be paired), so we can simplify the model:
[Image of the simplified tiles: |XX| + |1| + |1| = |UUUUUU|]
This shows that the model is balanced and x = 1 is a valid solution to the equation.
Therefore, the correct answer is to put 1 x-tile and 6 unit tiles on the model.
incorrect
I apologize for the confusion. Can you please specify which part of my explanation was incorrect and provide the correct solution? I'm here to help, and I want to make sure that I give you accurate information.
the awnser was incorrect
I apologize for the error in the previous answer.
To model the given equation, Juanita can represent 3x with three green x-tiles, 2 with two yellow unit tiles, and -x with one red x-tile.
[Image of the tiles: |XXX| + |YY| + |YY| = |RX| + |UUUUUU|]
Now, we need to balance the equation by moving tiles between sides. We can do this by adding one green x-tile to both sides and by adding four yellow unit tiles to the right side (since we need a total of six yellow unit tiles to balance the equation).
[Image of the balanced tiles: |XXX| + |YY| + |YY| + |X| = |RX| + |UU| + |UU| + |UU| + |UU|]
Now, we can eliminate the zero pair of x-tiles and -x-tiles:
[Image of the simplified tiles: |XX| + |YY| + |YY| = |UUUUUU|]
This shows that the model is balanced. Therefore, the correct answer is to put one green x-tile and four yellow unit tiles on the left side of the equal sign and one red x-tile and six yellow unit tiles on the right side of the equal sign.
What is the value of c in the equation 12 c minus 53 = 91?
We can solve for c in the given equation using algebraic methods:
12c - 53 = 91
Add 53 to both sides:
12c = 144
Divide by 12:
c = 12
Therefore, the solution to the equation 12c - 53 = 91 is c = 12.