Question

1. if the sum of twice a number and -12 is multiplied by 2, the result if 11 greater than the opposite of the number. find the number.
2. find a number which decreased by 42 equals 5 times its opposite.
3. find a number which decreased by 21 equals twice the opposite of the number.
4. the sum of 3 times a number and 70 equaled -50. find the number.
5. if the product of 3 and a number is increased by 7, the result is 23 greater than the number. find the number.
6. twice the sum of 3 times a number and 60 is 155 greater than the opposite of the number. find the number.
7. if the product of 5 and a number is increased by 9 and this sum is multiplied by 3, the result is 11 greater than the opposite of the number. find the number.
8. if the product of 5 and a number is increased by 8, the result is -42. what is the number?
9. if the product of 6 and a number is decreased by 5, the result is -35. what is the number?

Explanation:

Let's solve question 15 as an example (you can ask for other questions too).

Step1: Define the variable

Let the number be \( x \).

Step2: Translate the problem into an equation

The product of 6 and the number is \( 6x \). Decreasing that by 5 gives \( 6x - 5 \). This equals -35, so the equation is \( 6x - 5 = -35 \).

Step3: Solve for \( x \)

Add 5 to both sides: \( 6x - 5 + 5 = -35 + 5 \), which simplifies to \( 6x = -30 \).
Divide both sides by 6: \( \frac{6x}{6} = \frac{-30}{6} \), so \( x = -5 \).

Answer:

The number is \(-5\)