Drag and drop the correct steps to solve the equation for x. Make sure to put the steps in order. Not all steps listed will be used. 12−3x=8−4(2x−6)12−3x=8−4(2x−6)
x = 4, 12 - 3x = 8 - 8x - 24, x = 28, 12 + 5x = 32, 12 - 3x = 32 - 8x, 5x = 20, 12 - 5x = - 16, 12 - 3x = - 16 - 8x, 12 - 3x = 8 - 8x + 24
1) Simplify the expression inside the parentheses: 2x - 6 becomes 2x - 6
2) Distribute the -4 to the terms inside the parentheses: -4(2x - 6) becomes -8x + 24
3) Combine like terms on the right side of the equation: 8 - 8x + 24 becomes 32 - 8x
4) Rewrite the equation with the combined terms: 12 - 3x = 32 - 8x
5) Simplify both sides of the equation: 12 - 3x stays as 12 - 3x
6) Isolate the x term on one side of the equation by adding 8x to both sides: 32 - 8x + 8x becomes 32
7) Combine like terms on the left side of the equation: 12 - 3x + 8x becomes 12 + 5x
8) Rewrite the equation with the combined terms: 12 + 5x = 32
9) Isolate the x term on one side of the equation by subtracting 12 from both sides: 12 + 5x - 12 becomes 0 + 5x
10) Combine like terms on the left side of the equation: 0 + 5x stays as 5x
11) Simplify both sides of the equation: 32 - 12 becomes 20
12) Solve for x by dividing both sides of the equation by 5: 5x/5 becomes x
The correct order of steps to solve the equation for x is:
4) Rewrite the equation with the combined terms: 12 - 3x = 32 - 8x
5) Simplify both sides of the equation: 12 - 3x stays as 12 - 3x
6) Isolate the x term on one side of the equation by adding 8x to both sides: 32 - 8x + 8x becomes 32
7) Combine like terms on the left side of the equation: 12 - 3x + 8x becomes 12 + 5x
8) Rewrite the equation with the combined terms: 12 + 5x = 32
9) Isolate the x term on one side of the equation by subtracting 12 from both sides: 12 + 5x - 12 becomes 0 + 5x
10) Combine like terms on the left side of the equation: 0 + 5x stays as 5x
11) Simplify both sides of the equation: 32 - 12 becomes 20
12) Solve for x by dividing both sides of the equation by 5: 5x/5 becomes x
Which equation has no solution? Select all that apply. (1 point) Responses 8k+38=−3(−6−4k)8k+38=−3(−6−4k) 8 k plus 38 is equal to negative 3 times open paren negative 6 minus 4 k close paren −2(w−2)=−3−2w−2(w−2)=−3−2w negative 2 times open paren w minus 2 close paren is equal to negative 3 minus 2 w 36−7y=−7(y−5)36−7y=−7(y−5) 36 minus 7 y is equal to negative 7 times open paren y minus 5 close paren −4(x+3)=−12−4x−4(x+3)=−12−4x negative 4 times open paren x plus 3 close paren is equal to negative 12 minus 4 x
To determine which equation has no solution, we need to simplify each equation and see if they lead to a contradiction.
1) 8k + 38 = -3(-6 - 4k)
Simplifying the right side: -3(-6 - 4k) = 18 + 12k
The equation becomes: 8k + 38 = 18 + 12k
Solving for k by subtracting 8k and 18 from both sides: 38 - 18 = 12k - 8k -> 20 = 4k
Dividing both sides of the equation by 4: 20/4 = k -> 5 = k
This equation has a solution: k = 5.
2) -2(w - 2) = -3 - 2w
Simplifying the left side: -2(w - 2) = -2w + 4
The equation becomes: -2w + 4 = -3 - 2w
Notice that both sides of the equation have the term -2w, which means it will cancel out when we combine like terms.
Combining like terms: -2w - 2w = -2w - 2w -> 0 = -3 + 4 -> 0 = 1
This equation leads to a contradiction, so it has no solution.
3) 36 - 7y = -7(y - 5)
Simplifying the right side: -7(y - 5) = -7y + 35
The equation becomes: 36 - 7y = -7y + 35
Notice that both sides of the equation have the term -7y, which means it will cancel out when we combine like terms.
Combining like terms: -7y + 7y = -7y + 7y -> 0 = 35
This equation leads to a contradiction, so it has no solution.
4) -4(x + 3) = -12 - 4x
Simplifying the left side: -4(x + 3) = -4x - 12
The equation becomes: -4x - 12 = -12 - 4x
Both sides of the equation have the same terms -4x and -12, which means they are equal.
This equation is an identity, meaning it is true for all values of x.
It does not have no solution.
Equations 2) and 3) have no solution.
Let's solve the equation step-by-step:
Step 1: Distribute -4 to (2x - 6) on the right side of the equation.
12 - 3x = 8 - 4(2x - 6)
12 - 3x = 8 - 8x + 24
Step 2: Simplify both sides of the equation.
12 - 3x = 32 - 8x
Step 3: Move -3x to the right side by adding 3x to both sides.
12 - 3x + 3x = 32 - 8x + 3x
12 = 32 - 5x
Step 4: Move 32 to the left side by subtracting 32 from both sides.
12 - 32 = 32 - 5x - 32
-20 = -5x
Step 5: Solve for x by dividing both sides by -5.
(-20) / (-5) = (-5x) / (-5)
4 = x
So, the solution to the equation 12 - 3x = 8 - 4(2x - 6) is x = 4.
To solve the equation for x, follow these steps:
Step 1: Distribute the -4 to the terms inside the parentheses.
12 - 3x = 8 - 4 * 2x + 4 * 6
Simplifying this gives:
12 - 3x = 8 - 8x + 24
Step 2: Combine like terms.
12 - 3x = 8 - 8x + 24
Simplifying this gives:
12 - 3x = 32 - 8x
Step 3: Bring the variable terms (those with x) to one side of the equation by adding or subtracting.
Subtract -8x from both sides:
12 - 3x + 8x = 32 - 8x - 8x
This simplifies to:
5x + 12 = 32
Step 4: Isolate the variable term by subtracting or adding.
Subtract 12 from both sides:
5x + 12 - 12 = 32 - 12
This simplifies to:
5x = 20
Step 5: Solve for x by dividing both sides by the coefficient of x.
Divide both sides by 5:
5x/5 = 20/5
This simplifies to:
x = 4
Therefore, the solution for the equation is x = 4.