Solve the equation for x. Make sure to show work.
12+3x=6x−4(x−5)
To start, we will distribute the -4 to each term inside the parentheses:
12 + 3x = 6x - 4x + 20
Simplifying further:
12 + 3x = 2x + 20
To isolate "x," we will subtract 2x from both sides:
12 + 3x - 2x = 2x + 20 - 2x
12 + x = 20
Finally, we subtract 12 from both sides:
12 + x - 12 = 20 - 12
x = 8
The solution to the equation is x = 8.
The freshman class raised funds for a school dance. It costs $3,000 to rent out the hall plus $15 per student for food and drinks. The freshman class raised $12,000. Write and solve an equation to determine how many students can attend the school dance.
Let's assume the number of students attending the dance is "x."
The total cost of renting the hall is $3000.
The cost of food and drinks per student is $15.
Therefore, the total cost of food and drinks for "x" students would be 15x.
The total cost of the dance, including hall rental and food and drinks, is given as $12000.
So, we can write the equation:
3000 + 15x = 12000
To solve the equation, we need to isolate "x." Subtracting 3000 from both sides of the equation gives:
15x = 12000 - 3000
15x = 9000
Next, divide both sides of the equation by 15 to solve for "x":
15x/15 = 9000/15
x = 600
Therefore, 600 students can attend the school dance.
To solve the equation 12 + 3x = 6x - 4(x - 5) for x, we will first simplify the equation using the distributive property.
12 + 3x = 6x - 4x + 20
Now, let's combine like terms:
12 + 3x = 2x + 20
Next, we want to isolate the variable x on one side of the equation. To do this, we'll subtract 2x from both sides:
12 + 3x - 2x = 2x + 20 - 2x
Simplifying further:
12 + x = 20
We can now isolate the variable x by subtracting 12 from both sides:
12 + x - 12 = 20 - 12
Simplifying:
x = 8
Therefore, the solution to the equation is x = 8.
To solve the equation 12 + 3x = 6x - 4(x - 5) for x and show the work, we'll follow these steps:
1. Start by simplifying both sides of the equation.
2. Apply the distributive property to eliminate the parentheses.
3. Combine like terms on both sides.
4. Isolate the variable x.
5. Solve for x.
Now let's go through each step in detail:
Step 1: Simplify both sides of the equation.
12 + 3x = 6x - 4x + 20
Step 2: Apply the distributive property to eliminate the parentheses.
12 + 3x = 6x - 4x + 20
12 + 3x = 2x + 20
Step 3: Combine like terms on both sides.
To combine the x terms, we move all x terms to one side of the equation:
12 + 3x - 2x = 2x - 2x + 20
This simplifies to:
12 + x = 20
Step 4: Isolate the variable x.
To isolate x, we need to get rid of the constant term 12 on the left side of the equation. We do this by subtracting 12 from both sides:
12 + x - 12 = 20 - 12
This simplifies to:
x = 8
Step 5: Solve for x.
After isolating x, we find that x = 8.
Therefore, the solution to the equation 12 + 3x = 6x - 4(x - 5) is x = 8.