Algebra Mastery

Answer explanation

To multiply the linear expressions (2x + 3)(x - 4), use the distributive property. The correct answer is 2x^2 - 5x - 12.

Tags

CCSS.HSA.APR.A.1

Answer explanation

To solve the equation, first distribute the 3 on the left side: 3x - 6 + 4 = 2x + 6. Combine like terms: 3x - 2 = 2x + 6. Subtract 2x from both sides: x - 2 = 6. Add 2 to both sides: x = 8. Therefore, x = 1 is the correct answer.

Answer explanation

To simplify the expression, add the exponents when multiplying like terms. 3x^2 * 4x^3 = 3 * 4 * x^(2+3) = 12x^5. Therefore, the correct answer is 12x^5.

Tags

CCSS.HSA.APR.A.1

Answer explanation

To rewrite the expression 6x^2 + 9x, factor out the common factor 3x to get 3x(2x + 3). Therefore, the correct choice is 3x(2x + 3).

Answer explanation

To solve the inequality 2x - 5 < 3, add 5 to both sides to get 2x < 8. Then divide by 2 to find x < 4. Therefore, the correct answer is x < 4.

Tags

CCSS.7.EE.B.4B

Answer explanation

To multiply the linear expressions (x + 5)(x - 2), we use the distributive property. This results in x^2 + 3x - 10, which matches the expression x^2 + 3x - 10 in the answer choices.

Tags

CCSS.HSA.APR.A.1

Answer explanation

To solve the equation, first, combine like terms: 4x - 2x = 5 + 7. This simplifies to 2x = 12. Then, divide by 2 to find x = 6. Therefore, the correct answer is x = 6.

Answer explanation

To simplify the expression, divide the coefficients (8/2) to get 4. Then subtract the exponents (5-2) to get x^3. Therefore, the simplified expression is 4x^3.

Tags

CCSS.8.EE.A.1

Answer explanation

To rewrite the expression, factor out the greatest common factor, which is 5x^2. This leaves us with 5x^2(2x + 3), which matches the correct answer choice.

Answer explanation

To solve the inequality -3x + 4 ≤ 1, first subtract 4 from both sides to get -3x ≤ -3. Then divide by -3 (a negative number, so flip the inequality sign) to get x ≥ 1. Therefore, the correct answer is x ≥ 1.

Tags

CCSS.7.EE.B.4B