Simplifying Algebraic Expressions Quiz For Grade 7

The given expression is a sum of two terms: 3x + 1 and 8x + 9. To simplify the expression, we can combine the like terms by adding the coefficients of x and the constants separately. Adding 3x and 8x gives us 11x, and adding 1 and 9 gives us 10. Therefore, the simplified expression is 11x + 10.

The given expression is a combination of like terms. The like terms in the expression are 3x and 2x, which can be combined to give 5x. However, there is also a -3x term in the expression. When we subtract 3x from 5x, we get 2x as the final answer.

The given expression is 3x - 5x. To simplify this expression, we need to combine like terms. In this case, the like terms are the ones with the same variable, which is x. When we subtract 5x from 3x, we get -2x. Therefore, the correct answer is -2x.

The given expression involves adding and subtracting the terms involving x and y. To simplify the expression, we combine like terms by adding the coefficients of x and y separately. In this case, the x terms are 2x and -7x, which combine to give -5x. The y terms are 5y and 8y, which combine to give 13y. Therefore, the simplified expression is -5x + 13y.

To solve the expression 4(x + 8) - 9, you can follow these steps:

Distribute the 4 to both terms inside the parentheses:

4(x + 8) = 4x + 32

Now, you have the expression: 4x + 32 - 9.

Subtract 9 from 32:

32 - 9 = 23

Now, you have the simplified expression: 4x + 23.

So, the solution is 4x + 23.

To simplify the expression, combine the like terms:

w terms: 3w + w = 4w

m terms: -m + 6m = 5m

Therefore, the simplified expression is 4w + 5m

The number 1 is known as the multiplicative identity because any number multiplied by 1 will result in the original number. In other words, 1 is the identity element for multiplication. When any number is multiplied by 1, it retains its value and does not change. This property is true for all numbers, making 1 the multiplicative identity.

The given equation, a + b = b + a, demonstrates the commutative property of addition. This property states that the order of the numbers being added does not affect the sum. In other words, when adding two numbers, it does not matter which number is added first, the result will be the same. This property is applicable to addition but not to subtraction, multiplication, or division. Therefore, the correct answer is the Commutative Property of Addition.

The given equation ab(c) = (ab)c represents the associative property of multiplication. This property states that the grouping of numbers being multiplied does not affect the final result. In this case, it means that multiplying a and b first and then multiplying the result by c will yield the same result as multiplying b and c first and then multiplying the result by a. This property holds true for multiplication, but not for addition or cumulative properties.

The given expression is -3(x + y) + 5(x - y). To simplify this expression, we can distribute the -3 and 5 to the terms inside the parentheses. Distributing -3 gives us -3x - 3y, and distributing 5 gives us 5x - 5y. Combining like terms, we have -3x + 5x - 3y - 5y, which simplifies to 2x - 8y. Therefore, the correct answer is 2x - 8y.