KYOTE Algebraic Reasoning 2

Question 1

Which value of x satisfies the equation 3(x − 4) = 2x + 1?

Accepted Answer

x = 13

Answer

Distribute: 3x − 12 = 2x + 1, then x = 13.

Question 2

A line passes through (0, −2) and has slope 4. What is its equation?

Accepted Answer

y = 4x − 2

Answer

Using slope-intercept form y = mx + b with m = 4 and b = −2 gives y = 4x − 2.

Question 3

Simplify: (2x²y)(3xy³)

Accepted Answer

6x³y⁴

Answer

Multiply coefficients (2·3 = 6) and add exponents: x^(2+1) = x³ and y^(1+3) = y⁴.

Question 4

Which inequality represents all real numbers less than −3 or greater than 5?

Accepted Answer

x < −3 or x > 5

Answer

Numbers outside the interval (−3, 5) satisfy x < −3 or x > 5.

Question 5

What is the slope of the line 5x − 2y = 10?

Accepted Answer

5/2

Answer

Solve for y: −2y = −5x + 10, so y = (5/2)x − 5, giving slope 5/2.

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