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.