Algebraic Properties and Equations Quiz

Answer explanation

To solve the equation 2x + 5 = 13, subtract 5 from both sides to get 2x = 8. Then, divide by 2 to find x = 4. Thus, the correct answer is x = 4.

Tags

TEKS.MATH.9-12.II.C.1

Answer explanation

To solve for x in the equation 3x - 7 = 2x + 8, first subtract 2x from both sides to get x - 7 = 8. Then, add 7 to both sides to find x = 15. Thus, the correct answer is x = 15.

Tags

TEKS.MATH.9-12.II.C.1

• Associative Property

• Distributive Property

• Commutative Property

• Identity Property

Answer explanation

The equation a + b = b + a illustrates the Commutative Property, which states that the order of addition does not affect the sum. This property allows us to rearrange terms freely in addition.

Tags

TEKS.MATH.9-12.II.C.1

Answer explanation

To solve for y in the equation 4y + 3 = 19, first subtract 3 from both sides to get 4y = 16. Then, divide both sides by 4 to find y = 4. Thus, the correct answer is y = 4.

Tags

TEKS.MATH.9-12.II.C.1

Answer explanation

To simplify 5(x + 2), distribute 5: 5 * x + 5 * 2 = 5x + 10. Thus, the equivalent expression is 5x + 10, which is the correct answer.

Tags

TEKS.MATH.9-12.II.C.1

Answer explanation

To solve for x in the equation x - 3 = 7, add 3 to both sides: x = 7 + 3. This simplifies to x = 10, which is the correct answer.

Tags

TEKS.MATH.9-12.II.C.1

• Distributive Property

• Associative Property

• Commutative Property

• Inverse Property

Answer explanation

The equation a(b + c) = ab + ac illustrates the Distributive Property, which states that multiplying a number by a sum is the same as multiplying each addend separately and then adding the results.

Tags

TEKS.MATH.9-12.II.C.1

Answer explanation

To solve the inequality 2x - 5 < 9, add 5 to both sides to get 2x < 14. Then, divide by 2 to find x < 7. Thus, the correct answer is x < 7.

Tags

TEKS.MATH.9-12.II.C.1

What is the solution to the system of equations: \[ \begin{cases} x + y = 8 \\ x - y = 2 \end{cases} \]

Answer explanation

To solve the system, add the equations: (x + y) + (x - y) = 8 + 2, giving 2x = 10, so x = 5. Substitute x into the first equation: 5 + y = 8, thus y = 3. The solution is x = 5, y = 3.

Tags

TEKS.MATH.9-12.II.C.1

Which of the following is the multiplicative identity?

Answer explanation

The multiplicative identity is the number that, when multiplied by any number, leaves that number unchanged. This number is 1, as multiplying any number by 1 results in the same number.

Tags

TEKS.MATH.9-12.II.C.1