Question

Solve an equation to find the number. 11. The difference of six times a number and 7 is -49 12. Negative sixteen plus the quotient of a number and -4 is –3. 13. The sum of two times a number and 11 is -7. 14. The total cost for a week at camp is $220. You have $140. You eam S16 for every item you sell in a fundraiser. Ilow many items do you need to sell to pay for a week at camp?​

Answer 1

The equations are solved using algebraic techniques, considering the appropriate signs during arithmetic operations. The solutions found are x = -7 for the first equation, x = -52 for the second, x = -9 for the third, and one needs to sell 5 items for the last situation.

Step-by-step explanation:

To solve the given equations and find the unknown number, we'll use algebraic techniques and apply the rules of arithmetic operations including addition, subtraction, multiplication, and division while keeping in mind the signs of the numbers involved.

1. The difference of six times a number and 7 is -49 can be written as the equation 6x - 7 = -49. To solve for x, add 7 to both sides to get 6x = -42 and then divide both sides by 6 to find x = -7.
2. Negative sixteen plus the quotient of a number and -4 is -3. The equation is -16 + x/-4 = -3. Multiplying both sides by -4 gives x + 64 = 12, so x = 12 - 64, which results in x = -52.
3. The sum of two times a number and 11 is -7 is represented by the equation 2x + 11 = -7. Subtract 11 from both sides to get 2x = -18 and then divide by 2 to get x = -9.
4. To determine how many items you need to sell to pay for a week at camp, we use the equation 140 + 16x = 220. Subtracting 140 from both sides gives us 16x = 80, and dividing both sides by 16 gives us x = 5. Hence, you need to sell 5 items.