1 Which property is used in the equation below?
12(x + 4) = 12x + 48
A Associative Property of Addition
B Commutative Property of Addition
C Distributive Property
D Reflexive Property
2 Which expression is equivalent to 3 x – 3 y?
A 3xy
B 3(x–y) C 3x–y D x–3y
3 What is the value of x when 3x < −2x + 15?
Ax>3 Bx<3 C x < 15 D x > 15
4 Rashad solved the inequality 2x + 4 ≥ 14 and determined that x could equal 5. Is Rashad correct?
A No,because x ≥ 5
B No,because x = 5
C Yes,because x ≥ 5
D Yes,because x ≤ 5
TX:07
What the answer to the whole test
so what is the answer
1 The property used in the equation 12(x + 4) = 12x + 48 is the Distributive Property. This property states that when a number is multiplied by the sum of two or more numbers, it is the same as multiplying the number by each term individually and then adding the results.
To see this property at work in the given equation, we can distribute the 12 to both terms inside the parentheses:
12(x + 4) = 12 * x + 12 * 4
This simplifies to:
12x + 48 = 12x + 48
As you can see, the Distributive Property was used.
2 The expression equivalent to 3x - 3y is option D, x - 3y. To simplify the expression, we can factor out a common factor of 3:
3x - 3y = 3(x - y)
This is the equivalent expression given in option D.
3 To find the value of x in the inequality 3x < -2x + 15, we can start by simplifying it and solving for x:
3x < -2x + 15
Adding 2x to both sides:
3x + 2x < 15
Combining like terms:
5x < 15
Finally, dividing both sides by 5:
x < 3
Therefore, the value of x that satisfies the inequality is option B, x < 3.
4 Rashad is not correct. The correct answer is option A, No, because x ≥ 5.
To solve the inequality 2x + 4 ≥ 14, we can start by subtracting 4 from both sides:
2x + 4 - 4 ≥ 14 - 4
This simplifies to:
2x ≥ 10
Dividing both sides by 2:
x ≥ 5
Therefore, x must be greater than or equal to 5, not just equal to 5.
1. You distributed 12
2. Same as number 1 above!
3. 5 x <15 divide both sides by 5
4. 10 + 4 = ?????