Combine like terms:
-3x^2+2x-4x^2-9+6x-2x^2+8
Solve for x:
8x-11= -11x+18
Solve for x:
-2(x-5)+7=z-8-5x
Solve for x:
(x-2)/5 - 3/2= (x+1)/10
Translate to an algebra statement; do not solve:
Seven times the difference of six and a twice a number yields the same result as the same number decreased by one.
I will be happy to critique your work. To solve for x, combine the terms that include x on one side and the constants on the other.
"Combining" like terms" means separately combining the terms with different powers of x, and the constants.
Seven times the difference of six and a twice a number yields the same result as the same number decreased by one.
How does this translate into a algebra statement?
I can answer 3x^2+2x-4x^2-9+6x-2x^2+8
first you want to combined all the squared problems whch is : 3x^2 -4x^2-2x^2
Since two negatives make a positive : 3x^2-4x^2 =7x^2
now subtract -2x^2 and that leaves for 5x^2
Now you combine all the numbers with variables : 2x +6x = 8x
so now we have
5x^2+ 8x
now we combine all the constant numbers -9+8= -1
answer 5x^2+8x -1
7(6-x2) = x2-1
Seven times the difference of six and a twice a number yields the same result as the same number decreased by one.
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The ratio of 7 more than a number to 2 less than that number is 13/4. Find the number
seven less than twice an unknown number
To combine like terms, you need to simplify the expression by combining the terms that have the same variable and exponent. Let's start with the expression:
-3x^2 + 2x - 4x^2 - 9 + 6x - 2x^2 + 8
First, group the terms with the same variable and exponent:
(-3x^2 - 4x^2 - 2x^2) + (2x + 6x) + (-9 + 8)
Now, combine the like terms within each group:
-9x^2 + 8x - 1
So, the combined form of the expression -3x^2 + 2x - 4x^2 - 9 + 6x - 2x^2 + 8 is -9x^2 + 8x - 1.
Moving on to solving equations:
To solve the equation 8x - 11 = -11x + 18 for x, let's isolate the variable on one side of the equation. We can do this by adding 11x to both sides and adding 11 to both sides:
8x + 11x - 11 = -11x + 11x + 18 + 11
Combining like terms:
19x - 11 = 29
Next, we can isolate x by adding 11 to both sides:
19x - 11 + 11 = 29 + 11
Simplifying:
19x = 40
Finally, divide both sides by 19 to solve for x:
x = 40/19
Therefore, the solution to the equation 8x - 11 = -11x + 18 is x = 40/19.
Now, let's solve the equation -2(x - 5) + 7 = z - 8 - 5x for x:
First, distribute the -2:
-2x + 10 + 7 = z - 8 - 5x
Combine like terms:
-2x + 17 = z - 8 - 5x
Now, group the x terms on one side:
-2x + 5x = z - 8 - 17
Combine:
3x = z - 25
Now, if you need to solve for x specifically, you would need more information about the variable z. Otherwise, you can say that the solution for x in terms of z is x = (z - 25)/3.
Next, let's solve the equation (x - 2)/5 - 3/2 = (x + 1)/10 for x:
First, let's get rid of the fractions by multiplying through by the least common denominator, which is 10:
10[(x - 2)/5] - 10(3/2) = 10[(x + 1)/10]
Simplifying:
2(x - 2) - 15 = x + 1
Expanding and simplifying further:
2x - 4 - 15 = x + 1
Combine like terms:
2x - 19 = x + 1
Now, to isolate x, we can subtract x from both sides and add 19 to both sides:
2x - x = 1 + 19
Simplifying:
x = 20
Therefore, the solution to the equation (x - 2)/5 - 3/2 = (x + 1)/10 is x = 20.
Now, let's translate the given statement into an algebraic equation:
"Seven times the difference of six and a twice a number yields the same result as the same number decreased by one."
Let's break it down step by step:
Seven times the difference of six and a twice a number: 7(6 - 2x)
The same number decreased by one: x - 1
Putting it all together, the algebraic equation is:
7(6 - 2x) = x - 1
Keep in mind that this is just the translation of the statement into an equation. To solve for x, you would need to carry out the necessary steps.