Canada Grade 8 Algebra Expressions and equations

Answer explanation

To simplify the expression, combine like terms: 3x + 4x - 2x = (3 + 4 - 2)x = 5x. Thus, the correct answer is 5x.

Answer explanation

To solve for x, first isolate x by subtracting 2x from both sides: 5x - 2x - 3 = 9. This simplifies to 3x - 3 = 9. Next, add 3 to both sides: 3x = 12. Finally, divide by 3: x = 4. The correct answer is x = 6.

Answer explanation

To simplify \(2(a + 3) - 4\), first distribute: \(2a + 6 - 4\). Then combine like terms: \(2a + 2\). Thus, the equivalent expression is \(2a + 2\), which is the correct choice.

Answer explanation

To find the value of y when x = 4, substitute 4 into the equation y = 3x + 2: y = 3(4) + 2 = 12 + 2 = 14. Thus, the correct answer is 14.

Answer explanation

The expression x^2 - 9 is a difference of squares, which factors as (x - 3)(x + 3). This is because a^2 - b^2 = (a - b)(a + b), where a = x and b = 3.

Answer explanation

To solve for x, first distribute: 4(x - 1) = 4x - 4. Then, set the equation: 4x - 4 = 2x + 6. Rearranging gives 2x = 10, so x = 5. Thus, the correct answer is x = 5.

Answer explanation

To find the coefficient of x in the expression 7x - 5 + 3x, combine the x terms: 7x + 3x = 10x. Thus, the coefficient of x is 10.

Answer explanation

To expand (x + 2)(x - 3), use the distributive property: x(x - 3) + 2(x - 3) = x^2 - 3x + 2x - 6 = x^2 - x - 6. Thus, the correct answer is x^2 - x - 6.

Answer explanation

To solve for x, subtract 2x from both sides: 3x - 2x + 7 = 10. This simplifies to x + 7 = 10. Next, subtract 7 from both sides: x = 3. Thus, the correct answer is x = 3.

Answer explanation

Distribute 5 into (2x - 3) to get 10x - 15. Then, add 4x: 10x - 15 + 4x = 14x - 15. Thus, the simplified expression is 14x - 15, which matches the correct answer.