Half the sum of a number and 10 is 8. Find the number.(1 point)
Responses
3
3
6
6
2
2
-2
-2
To find the number, we can set up the equation "half the sum of a number and 10 is 8" as:
(1/2)(x + 10) = 8
Now, we can solve for x by multiplying both sides of the equation by 2 to eliminate the fraction:
x + 10 = 16
Next, we can isolate x by subtracting 10 from both sides:
x = 6
Therefore, the number is 6.
To find the number, we need to solve the equation given:
"Half the sum of a number and 10 is 8."
Let's break down the equation:
The sum of a number and 10 is written as "(number + 10)."
Half of this sum is written as "(1/2) * (number + 10)."
According to the equation, this half sum is equal to 8; thus, we can write the equation:
(1/2) * (number + 10) = 8
To solve for the number, we can follow these steps:
1. Multiply both sides of the equation by 2 to remove the fraction:
2 * (1/2) * (number + 10) = 2 * 8
Simplifying gives us:
number + 10 = 16
2. Subtract 10 from both sides of the equation to isolate the number:
number + 10 - 10 = 16 - 10
Simplifying further gives us:
number = 6
Therefore, the number is 6.
John buys 8 packs of cookies at the grocery store. The cookies are on sale for 50 cents off per pack. He spends $20. Which equation can be used to find the original cost of a box of cookies, c?(1 point)
Responses
8(c+0.50)=208 times open paren c plus 0 point 5 0 close paren is equal to 20
8c−0.50=208 c minus 0 point 5 0 is equal to 20
8(c−0.50)=208 times open paren c minus 0 point 5 0 close paren is equal to 20
8−0.50c=20
The correct equation to find the original cost of a box of cookies, c, is:
8(c - 0.50) = 20.
Given the equation 8(n+6)=104, identify the real-world problem that corresponds to this equation.(1 point)
Responses
The real-world problem that corresponds to the equation 8(n+6)=104 is not provided.
Which equation corresponds to the following problem?
(1 point)
Responses
8(2n+6)=1048 times open paren 2 n plus 6 close paren is equal to 104
8(n+6)=1048 times open paren n plus 6 close paren is equal to 104
2n+6=82 n plus 6 is equal to 8
8+n+n+6=104
The equation that corresponds to the given problem is: 8(n+6)=104
Consider this equation:
4(3x−2)=−24
Part 1. What is your first step in solving this equation? Remember, there is more than one way to solve this equation.
Part 2. How would you isolate the variable and solve for x after you have completed Part 1?
You do not need to solve the problem. Simply, describe your process.
**Please label Part 1 and Part 2 in your answer.**
Part 1: The first step in solving this equation is to distribute the 4 to each term inside the parentheses. This can be done using the distributive property.
Part 2: After distributing the 4, the equation becomes 12x - 8 = -24. To isolate the variable, we can add 8 to both sides of the equation to move the -8 term to the right side. This gives us 12x = -16. Finally, to solve for x, we divide both sides of the equation by 12, resulting in x = -16/12 or x = -4/3.