Expressions, Equations and Inequalities I am struggling can someone please explain how to get the correct answer choice thank you!

1. Which of the following is equal to (3x/5-7)+7

5x/3
3x/5
3x-35/5
(3x-7)+35

5. name the property of real numbers illustrated by the equation.
(2+square root 5)+3=2+(square root 5+3)

communative prop of mult
asso prop of mult
asso prop of add
dist prop

6. pi times 7=7 times pi

closure
assoc prop mul
com prop mul
com prop add

12. James has $40 to spend. He wants to buy two tickets to a show. He has to spend $7 to get to where tickets are sold. 2x +7 less than or equal to 40.
what is the solution to the ineqaulity?

x lessthan equal to 23.5
x less than equal to 16.5
x gtet 23.5
x gtet 16.5

Sorry my bad

1. c
5. c
6. b
12.b

You did not indicate what your choices are

1B

5C
6C
12B

1. To simplify the expression (3x/5 - 7) + 7, you can follow these steps:

Step 1: Combine the like terms in the parentheses: (3x/5 - 7) + 7 = (3x/5 - 7/1) + 7/1

Step 2: Find a common denominator for the fractions in the expression. The LCM (Least Common Multiple) of 5 and 1 is 5.

Step 3: Rewrite the fractions with the common denominator: (3x/5 - 7/1) + 7/1 = (3x/5 - 7/1) + (7/1 * 5/5) = (3x/5 - 7/1) + 35/5

Step 4: Add the fractions with the same denominator: (3x/5 - 7/1) + 35/5 = (3x - 35 + 35)/5 = (3x/5)

Therefore, the correct answer choice is 3x/5.

5. To determine the property of real numbers illustrated by the equation (2 + √5) + 3 = 2 + (√5 + 3), you can analyze the properties of real numbers:

- The commutative property of multiplication states that a*b = b*a. But since there is no multiplication involved in the equation, it cannot be the commutative property of multiplication.

- The associative property of multiplication states that (a*b)*c = a*(b*c). Similarly, since there is no multiplication involved, it cannot be the associative property of multiplication.

- The associative property of addition states that (a+b)+c = a+(b+c). This property is illustrated by the given equation: (2 + √5) + 3 = 2 + (√5 + 3). The order of addition in both cases does not change the result, and therefore, the correct answer choice is the associative property of addition.

6. To identify the property of real numbers in the equation pi times 7 = 7 times pi, you can analyze the properties of real numbers:

- Closure property states that if a and b are real numbers, then a+b and a*b are also real numbers. However, the equation does not involve addition or multiplication between pi and 7 or 7.

- The associative property of multiplication states that (a*b)*c = a*(b*c). But the equation does not involve any multiplication in that form.

- The commutative property of multiplication states that a*b = b*a. This property is illustrated by the given equation: pi times 7 = 7 times pi. The order of multiplication does not change the result, and therefore, the correct answer choice is the commutative property of multiplication.

12. To find the solution to the inequality 2x + 7 ≤ 40, you can follow these steps:

Step 1: Subtract 7 from both sides of the inequality: 2x + 7 - 7 ≤ 40 - 7

Step 2: Simplify: 2x ≤ 33

Step 3: Divide both sides of the inequality by 2 (since it is multiplied by x): (2x)/2 ≤ 33/2

Step 4: Simplify: x ≤ 16.5

Therefore, the correct answer choice is x ≤ 16.5.