Question
Which is a solution to the equation `-2x+10=-30`?
Answers
Answer
Solve the equation
-2(6x-5)=4
-2(6x-5)=4
Answer
Solve the equation
4(x-5)+x=10
4(x-5)+x=10
Answer
A consultant charges $45 for each hour she works on a consultation, plus a flat $30 consulting fee. Which equation could be used to find how many hours of work are included in a $210 bill for a consultation?
Answer
Solve this equation. Be sure to show at least 2 steps
-2x+9-3x=16
-2x+9-3x=16
Answer
solve
-x+5+6x=2+5x+3
is it identity or no solution
-x+5+6x=2+5x+3
is it identity or no solution
Answer
Austin worked out the problem to the left and got an answer of x=7
Lisa thinks he made a mistake and the answer should be x=1
Who is correct or are they both wrong? Why?
Lisa thinks he made a mistake and the answer should be x=1
Who is correct or are they both wrong? Why?
Answer
solve
-3(-5x+2)+x-3=39
-3(-5x+2)+x-3=39
Answer
solve
3x+5=-2x+15
3x+5=-2x+15
Answered by
GPT 3.5
To solve for x in the equation -2x + 10 = -30, we can start by isolating the variable x by moving the constant to the other side of the equation. Add 30 to both sides:
-2x + 10 + 30 = -30 + 30
This simplifies to:
-2x + 40 = 0
Now, to eliminate the coefficient -2, we can divide both sides of the equation by -2:
(-2x + 40) / -2 = 0 / -2
This leads to:
x - 20 = 0
Finally, isolate x by moving the constant to the other side of the equation. Add 20 to both sides:
x - 20 + 20 = 0 + 20
This simplifies to:
x = 20
Therefore, the solution to the equation -2x + 10 = -30 is x = 20.
-2x + 10 + 30 = -30 + 30
This simplifies to:
-2x + 40 = 0
Now, to eliminate the coefficient -2, we can divide both sides of the equation by -2:
(-2x + 40) / -2 = 0 / -2
This leads to:
x - 20 = 0
Finally, isolate x by moving the constant to the other side of the equation. Add 20 to both sides:
x - 20 + 20 = 0 + 20
This simplifies to:
x = 20
Therefore, the solution to the equation -2x + 10 = -30 is x = 20.
Answered by
GPT 3.5
To solve the equation -2(6x-5) = 4, we first distribute -2 to the terms inside the parentheses:
-12x + 10 = 4
Next, subtract 10 from both sides of the equation to isolate the variable:
-12x = 4 - 10
-12x = -6
Finally, divide both sides of the equation by -12 to solve for x:
x = -6 / -12
x = 1/2
Therefore, the solution to the equation -2(6x-5) = 4 is x = 1/2.
-12x + 10 = 4
Next, subtract 10 from both sides of the equation to isolate the variable:
-12x = 4 - 10
-12x = -6
Finally, divide both sides of the equation by -12 to solve for x:
x = -6 / -12
x = 1/2
Therefore, the solution to the equation -2(6x-5) = 4 is x = 1/2.
Answered by
GPT 3.5
To solve the equation 4(x-5) + x = 10, we begin by distributing the 4 to the terms inside the parentheses:
4x - 20 + x = 10
Combining like terms, we have:
5x - 20 = 10
Next, we isolate the variable by adding 20 to both sides of the equation:
5x - 20 + 20 = 10 + 20
Simplifying further:
5x = 30
Finally, to solve for x, we divide both sides of the equation by 5:
x = 30 / 5
Simplifying the division:
x = 6
Thus, the solution to the equation 4(x-5) + x = 10 is x = 6.
4x - 20 + x = 10
Combining like terms, we have:
5x - 20 = 10
Next, we isolate the variable by adding 20 to both sides of the equation:
5x - 20 + 20 = 10 + 20
Simplifying further:
5x = 30
Finally, to solve for x, we divide both sides of the equation by 5:
x = 30 / 5
Simplifying the division:
x = 6
Thus, the solution to the equation 4(x-5) + x = 10 is x = 6.
Answered by
GPT 3.5
Let's denote the number of hours the consultant works on the consultation as "h".
The consultant charges $45 per hour, so the total cost for the hours worked would be 45h.
Additionally, there is a flat consulting fee of $30.
Therefore, the total cost for the consultation can be represented by the equation:
45h + 30 = 210
In this equation, "h" represents the number of hours of work included in the $210 bill for the consultation.
The consultant charges $45 per hour, so the total cost for the hours worked would be 45h.
Additionally, there is a flat consulting fee of $30.
Therefore, the total cost for the consultation can be represented by the equation:
45h + 30 = 210
In this equation, "h" represents the number of hours of work included in the $210 bill for the consultation.
Answered by
GPT 3.5
To solve the equation -2x + 9 - 3x = 16, we can combine like terms by adding the x terms together and moving the constants to one side of the equation.
First, combine the x terms:
-2x - 3x + 9 = 16
This simplifies to:
-5x + 9 = 16
Next, move the constant 9 to the other side of the equation by subtracting 9 from both sides:
-5x + 9 - 9 = 16 - 9
This simplifies to:
-5x = 7
Finally, to solve for x, divide both sides of the equation by -5:
(-5x) / -5 = 7 / -5
This gives us:
x = -7/5
Therefore, the solution to the equation -2x + 9 - 3x = 16 is x = -7/5.
First, combine the x terms:
-2x - 3x + 9 = 16
This simplifies to:
-5x + 9 = 16
Next, move the constant 9 to the other side of the equation by subtracting 9 from both sides:
-5x + 9 - 9 = 16 - 9
This simplifies to:
-5x = 7
Finally, to solve for x, divide both sides of the equation by -5:
(-5x) / -5 = 7 / -5
This gives us:
x = -7/5
Therefore, the solution to the equation -2x + 9 - 3x = 16 is x = -7/5.
Answered by
GPT 3.5
To solve the equation -x + 5 + 6x = 2 + 5x + 3, we can combine like terms and simplify:
First, combine the x terms on the left side of the equation:
5x - x + 5 = 2 + 5x + 3
This simplifies to:
4x + 5 = 2 + 5x + 3
Next, combine the constants on both sides of the equation:
4x + 5 = 5x + 5
Now, subtract 4x from both sides to isolate the variable:
4x - 4x + 5 = 5x - 4x + 5
This simplifies to:
5 = x + 5
Next, subtract 5 from both sides of the equation:
5 - 5 = x + 5 - 5
This simplifies to:
0 = x
Therefore, the solution to the equation -x + 5 + 6x = 2 + 5x + 3 is x = 0.
Since we found a unique solution for x, this equation has a solution and is not an identity or no solution.
First, combine the x terms on the left side of the equation:
5x - x + 5 = 2 + 5x + 3
This simplifies to:
4x + 5 = 2 + 5x + 3
Next, combine the constants on both sides of the equation:
4x + 5 = 5x + 5
Now, subtract 4x from both sides to isolate the variable:
4x - 4x + 5 = 5x - 4x + 5
This simplifies to:
5 = x + 5
Next, subtract 5 from both sides of the equation:
5 - 5 = x + 5 - 5
This simplifies to:
0 = x
Therefore, the solution to the equation -x + 5 + 6x = 2 + 5x + 3 is x = 0.
Since we found a unique solution for x, this equation has a solution and is not an identity or no solution.
Answered by
GPT 3.5
To determine who is correct or if they are both wrong, we will substitute their proposed solutions into the original equation and verify if they satisfy the equation.
Let's substitute x=7 into the original equation:
-x + 5 + 6x = 2 + 5x + 3
-7 + 5 + 6(7) = 2 + 5(7) + 3
-7 + 5 + 42 = 2 + 35 + 3
40 = 40
This shows that x=7 is a valid solution.
Now, let's substitute x=1 into the original equation:
-1 + 5 + 6(1) = 2 + 5(1) + 3
-1 + 5 + 6 = 2 + 5 + 3
10 = 10
This shows that x=1 is also a valid solution.
Therefore, both Austin and Lisa are correct as x=7 and x=1 both satisfy the original equation.
Let's substitute x=7 into the original equation:
-x + 5 + 6x = 2 + 5x + 3
-7 + 5 + 6(7) = 2 + 5(7) + 3
-7 + 5 + 42 = 2 + 35 + 3
40 = 40
This shows that x=7 is a valid solution.
Now, let's substitute x=1 into the original equation:
-1 + 5 + 6(1) = 2 + 5(1) + 3
-1 + 5 + 6 = 2 + 5 + 3
10 = 10
This shows that x=1 is also a valid solution.
Therefore, both Austin and Lisa are correct as x=7 and x=1 both satisfy the original equation.
Answered by
GPT 3.5
To solve the equation -3(-5x+2)+x-3=39, we can simplify the expression on the left side and isolate the variable x.
First, distribute -3 to the terms inside the parentheses:
15x - 6 + x - 3 = 39
Combine like terms:
16x - 9 = 39
Next, move the constant -9 to the other side of the equation by adding 9 to both sides:
16x - 9 + 9 = 39 + 9
Simplify further:
16x = 48
Finally, to solve for x, divide both sides of the equation by 16:
(16x) / 16 = 48 / 16
This gives us:
x = 3
Therefore, the solution to the equation -3(-5x+2)+x-3=39 is x = 3.
First, distribute -3 to the terms inside the parentheses:
15x - 6 + x - 3 = 39
Combine like terms:
16x - 9 = 39
Next, move the constant -9 to the other side of the equation by adding 9 to both sides:
16x - 9 + 9 = 39 + 9
Simplify further:
16x = 48
Finally, to solve for x, divide both sides of the equation by 16:
(16x) / 16 = 48 / 16
This gives us:
x = 3
Therefore, the solution to the equation -3(-5x+2)+x-3=39 is x = 3.
Answered by
GPT 3.5
To solve the equation 3x + 5 = -2x + 15, we can begin by isolating the variable x.
First, add 2x to both sides of the equation to eliminate the -2x term:
3x + 2x + 5 = -2x + 2x + 15
This simplifies to:
5x + 5 = 15
Next, subtract 5 from both sides of the equation to isolate the variable:
5x + 5 - 5 = 15 - 5
Simplifying further:
5x = 10
Finally, to solve for x, divide both sides of the equation by 5:
(5x) / 5 = 10 / 5
This gives us:
x = 2
Therefore, the solution to the equation 3x + 5 = -2x + 15 is x = 2.
First, add 2x to both sides of the equation to eliminate the -2x term:
3x + 2x + 5 = -2x + 2x + 15
This simplifies to:
5x + 5 = 15
Next, subtract 5 from both sides of the equation to isolate the variable:
5x + 5 - 5 = 15 - 5
Simplifying further:
5x = 10
Finally, to solve for x, divide both sides of the equation by 5:
(5x) / 5 = 10 / 5
This gives us:
x = 2
Therefore, the solution to the equation 3x + 5 = -2x + 15 is x = 2.