Grade 8 Algebra Quiz: Linear Equations

Answer explanation

To solve for x in the equation 3x + 5 = 20, subtract 5 from both sides to get 3x = 15. Then, divide both sides by 3 to find x = 5. Thus, the correct answer is x = 5.

Answer explanation

To solve the inequality 2x - 4 < 10, add 4 to both sides to get 2x < 14. Then, divide by 2 to find x < 7. Thus, the correct answer is x < 7.

Answer explanation

To find the value of y when x = 4, substitute 4 into the equation y = 2x + 3: y = 2(4) + 3 = 8 + 3 = 11. Therefore, the correct answer is y = 11.

Answer explanation

To solve for x, first isolate x by subtracting 3x from both sides: 5x - 3x - 2 = 6. This simplifies to 2x - 2 = 6. Next, add 2 to both sides: 2x = 8. Finally, divide by 2 to find x = 4, which is the correct answer.

Answer explanation

To solve the inequality 4x + 1 ≥ 9, subtract 1 from both sides to get 4x ≥ 8. Then, divide by 4 to find x ≥ 2. Thus, the correct solution is x ≥ 2.

Answer explanation

The slope of a line in the equation y = mx + b is represented by 'm'. In this case, the equation is y = -3x + 7, so the slope is -3. Therefore, the correct answer is -3.

Answer explanation

To solve for x, first distribute: 3(x - 2) = 3x - 6. Set the equation: 3x - 6 = 2x + 4. Rearranging gives x = 10. Thus, x = 4 is the correct answer.

Answer explanation

To solve the inequality -2x + 5 ≤ 1, subtract 5 from both sides to get -2x ≤ -4. Dividing by -2 reverses the inequality, yielding x ≥ 2. Thus, the correct answer is x ≥ 2.

Answer explanation

To find the y-intercept of the line y = \frac{1}{2}x - 3, set x = 0. This gives y = -3. Therefore, the y-intercept is -3.

Answer explanation

To solve for x, rearrange the equation: x + 4 = 2x - 3. Subtract x from both sides: 4 = x - 3. Then add 3 to both sides: 7 = x. Thus, the value of x is 7.