can anyone help me with these 3 problems I am trying to check my daughters hoime work it has bee na few years.

1. The sum of n and twenty -two, multiplied by three, is 78

2. the product of z and 17 is less than or equal to the difference of twenty -one minus z.

3.two increased by eight times a number is equal to the number divided by 5

Ok, we have
(1) (n + 22)*3 = 78. Divide both sides by 3 to get
n + 22=26 now subtract 22 from both sides to get n=4
(2) z*17 <= 21 - z add z to both sides to get
z*17 + z <= 21 or
z*18 <= 21 now divide both sides by 18 to get
z<=21/18 or z <= 7/6
(3) Denote the number by n then
2 + 8n = n/5 multiply both sides by 5 to get
10 + 40n = n now subtract n from both sides and subtract 10 from both sides to get
39n = -10 so n=-10/39

To solve the problems, let's go step by step:

1. The first problem states that "The sum of n and twenty-two, multiplied by three, is 78." So we can write this as an equation: (n + 22) * 3 = 78. To solve for n, we need to isolate it.

- First, divide both sides of the equation by 3: (n + 22) = 26.
- Next, subtract 22 from both sides to get n = 4.

Therefore, the solution to the first problem is n = 4.

2. The second problem states: "The product of z and 17 is less than or equal to the difference of twenty-one minus z." Let's write this as an equation: z * 17 ≤ 21 - z.

- To solve for z, we need to isolate it. Start by adding z to both sides of the equation: z * 17 + z ≤ 21.
- Combine like terms: 18z ≤ 21.
- Finally, divide both sides by 18: z ≤ 21/18 or z ≤ 7/6.

Therefore, the solution to the second problem is z ≤ 7/6.

3. The third problem states: "Two increased by eight times a number is equal to the number divided by 5." Let's represent the number by n. The equation is: 2 + 8n = n/5.

- To solve for n, let's eliminate the fraction. Multiply both sides of the equation by 5 to get rid of the denominator: 10 + 40n = n.
- Subtract n from both sides: 10 + 39n = 0.
- Move the constant term to the other side: 39n = -10.
- Finally, divide both sides by 39: n = -10/39.

Therefore, the solution to the third problem is n = -10/39.

I hope that helps! Let me know if you have any more questions.

What number should be added to both sides of the equation x − 7/8 = −5x − 7/8 = −5 to find the value of x?(1 point)