Steven cuts a 25-foot board into 2 pieces. One piece is 4 feet more than 2 times the length of the second piece. What is the length of the second, shorter, piece of the board?
Let's call the length of the second piece "x".
We know that the first piece is 4 feet more than 2 times the length of the second piece, so we can write an equation:
Length of first piece = 2x + 4
We also know that the two pieces must add up to the original length of the board, which was 25 feet:
Length of first piece + Length of second piece = 25
We can use the first equation to substitute the expression 2x + 4 for the length of the first piece in the second equation:
(2x + 4) + x = 25
Now we can solve for x:
3x + 4 = 25
3x = 21
x = 7
Therefore, the length of the second, shorter, piece of the board is 7 feet.
The model below represents 2 x + 1 = negative x + 4.
2 green long tiles and 1 green square tile = 1 long red tile and 4 square green tiles
What is the value of x when solving the equation 2 x + 1 = negative x + 4 using the algebra tiles?
To represent 2x + 1 using algebra tiles, we need 2 green long tiles and 1 green square tile.
To represent -x + 4, we need 1 red long tile and 4 green square tiles.
We want to balance the two sides of the equation so that they are equivalent. Since we have an extra red long tile on the right side, we can add a green square tile to the left side:
2 green long tiles and 1 green square tile + 1 green square tile = 1 red long tile and 4 green square tiles
Now we can see that the left side has 2 green long tiles, which represents 2x, so:
2x + 1 = -x + 4
becomes
2 green long tiles = -x + 3
We can see that 1 red long tile is equal to -x, so we have:
2 green long tiles + 1 red long tile = 3 green square tiles
Since we have 2 green long tiles, we can take away 2 green square tiles from both sides:
1 red long tile = 1 green square tile
Therefore, x = -1, since 1 red long tile is equal to -1.
Viktoriya solved an equation as shown below.
5 (x minus 2) minus 3 x = 2 (x minus 3) minus 16. 5 x minus 10 minus 3 x = 2 x minus 6 minus 16. 2 x minus 10 = 2 x minus 22. negative 10 = negative 22.
She says that the equation has infinitely many solutions. Which describes Viktoriya’s error?
Viktoriya's error is that she incorrectly simplified the equation 5x - 10 - 3x = 2x - 6 - 16 to 2x - 10 = 2x - 22.
In fact, simplifying the left side gives 2x - 10, while simplifying the right side gives 2x - 22.
Therefore, we end up with the equation 2x - 10 = 2x - 22, which simplifies to -10 = -22.
This statement is false, as -10 is not equal to -22.
Therefore, the equation does not have infinitely many solutions, and Viktoriya's error was in her simplification of the equation.
please chgoose the awnser forf the previoius question Viktoriya used the distributive property incorrectly when she found the solution.
Viktoriya should have said that the equation has no solution.
Viktoriya should have continued to solve the equation to find that x = 0.
Viktoriya should have said that the equation has one unique solution.
Viktoriya should have said that the equation has no solution.
thanks buddy
You're welcome!
Which finds the solution to the equation represented by the model below?
2 x tiles = 1 x tile and 3 positive 1 tiles
removing 1 x-tile from each side
removing 3 unit tiles from the right side
adding 3 positive unit tiles to each side
arranging the tiles into equal groups to match the number of x-tiles