Order the the steps to solve the equation for x. Make sure to put the steps in order. Not all steps will be used.
-6(x + 3) + 4x = -6x + 30
Step 1 Step 2 Step 3 Step 4 Final Answer
x = 12
-6x -18 + 4x = -6 x + 30
-6x +3 + 4x = -6x + 30
4x - 18 = 30
-8x + 3 = 30
-2x -18 = -6x + 30
4x = 48
-8x = 27
x = -27/8
x = 12
-6x -18 + 4x = -6 x + 30
-6x +3 + 4x = -6x + 30
4x - 18 = 30
-8x + 3 = 30
-2x -18 = -6x + 30
4x = 48
-8x = 27
x = -27/8
Step 1: Distribute -6 to the terms inside the parentheses:
-6x - 18 + 4x = -6x + 30
Step 2: Combine like terms on each side of the equation:
-2x -18 = -6x + 30
Step 3: Move all the x terms to one side by adding 6x to both sides:
4x - 18 = 30
Step 4: Move all the constant terms to the other side by adding 18 to both sides:
4x - 18 + 18 = 30 + 18
Final Answer: 4x = 48
Solve the following equation for w.
6 - 3w = 2 - 4w + w
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No Solution
Infinitely Many Solutions
w = -4
w = 0
w = 2/3
To solve the equation for w, we need to combine like terms and isolate the variable.
Step 1: Combine like terms on each side of the equation:
6 - 3w = 2 - 4w + w
Step 2: Combine the constant terms on each side:
6 - 3w = 2 - 3w
Step 3: Move all the w terms to one side by adding 3w to both sides:
6 = 2
Step 4: Since the equation simplifies to 6 = 2, which is not true, the equation has no solution.
Final Answer: No Solution
Tom and Jerry were at a State Fair. They each got a ticket for the Merry Go Round. Tom got a funnel cake, and Jerry got a churro. Tom had a certificate for $3 off the cost. Jerry paid the rest, which came to $12. Each Merry Go Round ticket was $5, and a funnel cake was $3.50. What equation represents this problem? What was the cost for a churro?
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5.00(2) +3.50 + x + 3.00 = 12.00; x = -4.50
5.00 + 3.50 + x - 3.00 = 12.00; x = 6.50
5.00(2) +3.50 + x - 3.00 = 12.00; x = 1.50
5.00 + 3.50 + x + 3 = 12.00; x = .50
Let's break down the problem and translate it into an equation.
Tom and Jerry each got a ticket for the Merry Go Round which cost $5 each. So, the total cost for the tickets would be $5 * 2 = $10.
Tom had a certificate for $3 off the cost, so we subtract $3 from the total cost:
$10 - $3 = $7
Tom also got a funnel cake which cost $3.50. So, we add $3.50 to the cost:
$7 + $3.50 = $10.50
Jerry paid the rest of the cost, which is $12. So, we subtract $10.50 from $12 to find the cost of the churro:
$12 - $10.50 = $1.50
Therefore, the equation representing this problem is:
5.00(2) + 3.50 + x - 3.00 = 12.00
where x represents the cost of the churro.
Final Answer: The cost for a churro is $1.50.
Solve the following equation:
3(h + 2) - 4 = 11
To solve the equation, we will follow the order of operations and isolate the variable h.
Step 1: Distribute the 3 to the terms inside the parentheses:
3h + 6 - 4 = 11
Step 2: Combine like terms:
3h + 2 = 11
Step 3: Move the constant term to the other side by subtracting 2 from both sides:
3h = 11 - 2
3h = 9
Step 4: Divide both sides by 3 to isolate the variable h:
h = 9/3
h = 3
Final Answer: The solution to the equation is h = 3.
Solve the following equation.
5x + 2 = 5(x - 2) + 12
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True
False
Open
To determine if the equation is true, false, or open, we need to simplify both sides of the equation and see if they are equal.
Let's simplify both sides of the equation:
Left side:
5x + 2
Right side:
5(x - 2) + 12
= 5x - 10 + 12
= 5x + 2
Now, we can see that both sides of the equation simplify to 5x + 2. Since they are equal, the equation is true.
Final Answer: True
Which ordered pair is a solution of the equation? Choose all that apply.
y = 6x - 4
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(0, 4)
(1, 2)
(-1, 10)
(2, 8)
(-2, -16)
(-1, -10)