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
The correct option is:
arranging the tiles into equal groups to match the number of x-tiles
This is because the model already represents the equation, with 2 x tiles on one side being equal to 1 x tile and 3 positive 1 tiles on the other side.
To find the solution to the equation, we need to make sure that there are the same number of x tiles on both sides.
Therefore, we need to arrange the tiles into equal groups to make sure that we have the same number of x tiles on both sides of the equation. This gives us:
x = 3
So the solution to the equation is x = 3.
Identify the method that will be used in solving for x.
5 + x = three-fourths
The method that will be used in solving for x is:
Subtract 5 from both sides of the equation, and then multiply both sides by 4/3 to isolate x.
The steps would be:
1. Subtract 5 from both sides:
5 + x - 5 = three-fourths - 5
x = three-fourths - 5
2. Convert the mixed number to an improper fraction:
three-fourths = 3/4
3. Simplify the right side:
three-fourths - 5 = 3/4 - 20/4
three-fourths - 5 = -17/4
4. Multiply both sides by 4/3 to isolate x:
4/3 * x = 4/3 * -17/4
x = -17/3
Therefore, the solution to the equation 5 + x = three-fourths is x = -17/3.
please choose an awnser for the previous quistion distributive property
multiplication property of equality
division property of equality
subtraction property of equality
The method that will be used in solving for x is:
Subtraction property of equality
The expression on the left side of an equation is shown below.
3 x + 9 = box
If the equation has no solution, which expression can be written in the box on the other side of the equation?
If the equation 3x + 9 = box has no solution, then the expression that can be written in the box on the other side of the equation would be any expression that is not equal to 3x + 9.
For example, we could write:
box = 3x + 8
or
box = 3x + 10
In general, as long as the expression in the box is not equal to 3x + 9, the equation will have no solution.
choose an awnser for the previous question
–9
–3
3 x
3 x + 9
The expression that can be written in the box on the other side of the equation would be any expression that is not equal to 3x + 9.
None of the given options satisfies this condition. Therefore, the correct answer is None of the above.
Which equation below would be best solved by using the addition property of equality?
f divided by 23 = 45
23 f = 45
f + 23 = 45
f minus 23 = 45
The equation that would best be solved by using the addition property of equality is:
f + 23 = 45
This is because we can use the addition property of equality to isolate the variable term (f) on one side of the equation and the constant term on the other side.
Using the addition property of equality, we can subtract 23 from both sides:
f + 23 - 23 = 45 - 23
f = 22
Therefore, the solution to the equation f + 23 = 45 is f = 22.