The solution to an addition problem is called the

1. The solution to an addition problem is called the _. Add -50-(-40)+( -60)+80
2. The solution to a subtraction problem is called the __. Subtract -10-(-19)
3. The solution to a multiplication problem is called the __. Multiply -2-3(-4)*5
4. The solution to a division problem is called the _. Divide 10÷ ¾
   Combine terms if possible, if not explain why
   5) 6x-8x
   6) x + x2

The Correct Answer and Explanation is :

1. The solution to an addition problem is called the sum.
   • For the expression −50−(−40)+(−60)+80-50 – (-40) + (-60) + 80, the calculation steps are: −50+40−60+80=10-50 + 40 – 60 + 80 = 10 Therefore, the sum is 10.
2. The solution to a subtraction problem is called the difference.
   • For the expression −10−(−19)-10 – (-19), the calculation steps are: −10+19=9-10 + 19 = 9 Therefore, the difference is 9.
3. The solution to a multiplication problem is called the product.
   • For the expression −2×−3×−4×5-2 \times -3 \times -4 \times 5, the calculation steps are: (−2)×(−3)=6(multiplying negative values gives a positive result)(-2) \times (-3) = 6 \quad \text{(multiplying negative values gives a positive result)} 6×(−4)=−24(multiplying by a negative value gives a negative result)6 \times (-4) = -24 \quad \text{(multiplying by a negative value gives a negative result)} −24×5=−120-24 \times 5 = -120 Therefore, the product is −120-120.
4. The solution to a division problem is called the quotient.
   • For the expression 10÷3410 \div \frac{3}{4}, this is equivalent to multiplying 10 by the reciprocal of 34\frac{3}{4}, which is 43\frac{4}{3}: 10×43=403≈13.3310 \times \frac{4}{3} = \frac{40}{3} \approx 13.33 Therefore, the quotient is 403\frac{40}{3} or approximately 13.33.

Now, let’s look at combining terms:

5. 6x−8x6x – 8x
   • Both terms contain the variable xx, so we combine them by adding the coefficients: 6x−8x=−2x6x – 8x = -2x Therefore, the simplified expression is −2x-2x.
6. x+x2x + x^2
   • This expression contains two terms: one with xx and one with x2x^2. Since they have different powers of xx, they cannot be combined. Therefore, the expression remains as x+x2x + x^2.

Explanation of combining terms:

When simplifying algebraic expressions, we combine like terms. Like terms are terms that have the same variable raised to the same power. For example:

• 6x6x and −8x-8x are like terms because both have the variable xx raised to the power of 1.
• However, xx and x2x^2 are not like terms, as xx is raised to the first power and x2x^2 is raised to the second power. They cannot be combined directly because they represent different powers of the variable xx.

To combine like terms, you simply add or subtract their coefficients. In the case of 6x−8x6x – 8x, the result is −2x-2x because the coefficients are 6 and -8. However, in expressions like x+x2x + x^2, where the terms involve different exponents, you leave the terms separate and do not combine them.