FTCE GK Mathematics Linear Equations and Inequalities Quiz

1. Solve for x: 3x + 7 = 22.

X = 5

X = 10

X = 3

X = 8

To solve for x in the equation 3x + 7 = 22, first subtract 7 from both sides, resulting in 3x = 15. Then, divide both sides by 3, yielding x = 5. This shows that when x is 5, the original equation holds true.

Explanation

To solve for x in the equation 3x + 7 = 22, first subtract 7 from both sides, resulting in 3x = 15. Then, divide both sides by 3, yielding x = 5. This shows that when x is 5, the original equation holds true.

2. Which ordered pair is a solution to 2x - y = 5?

(0, -5)

(3, 1)

(2, 4)

(1, 2)

To determine if an ordered pair is a solution to the equation 2x - y = 5, substitute the x and y values into the equation. For (3, 1), substituting gives 2(3) - 1 = 6 - 1 = 5, which satisfies the equation. Therefore, (3, 1) is a valid solution.

Explanation

To determine if an ordered pair is a solution to the equation 2x - y = 5, substitute the x and y values into the equation. For (3, 1), substituting gives 2(3) - 1 = 6 - 1 = 5, which satisfies the equation. Therefore, (3, 1) is a valid solution.

3. Solve the inequality: -2x + 8 > 4.

X < 2

X > 2

X > 6

X < 6

To solve the inequality -2x + 8 > 4, first subtract 8 from both sides to get -2x > -4. Dividing both sides by -2 reverses the inequality, resulting in x

Explanation

To solve the inequality -2x + 8 > 4, first subtract 8 from both sides to get -2x > -4. Dividing both sides by -2 reverses the inequality, resulting in x

4. What is the slope of the line passing through (2, 3) and (5, 9)?

2

3

1

4

To find the slope of a line passing through two points, use the formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \). For the points (2, 3) and (5, 9), substituting gives \( m = \frac{9 - 3}{5 - 2} = \frac{6}{3} = 2 \). Thus, the slope is 2.

Explanation

To find the slope of a line passing through two points, use the formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \). For the points (2, 3) and (5, 9), substituting gives \( m = \frac{9 - 3}{5 - 2} = \frac{6}{3} = 2 \). Thus, the slope is 2.

5. Find the x-intercept of y = 2x - 6.

3

-6

2

-3

To find the x-intercept, set y to 0 in the equation y = 2x - 6. This gives the equation 0 = 2x - 6. Solving for x, add 6 to both sides to get 6 = 2x, and then divide by 2, resulting in x = 3. Thus, the x-intercept is 3.

Explanation

To find the x-intercept, set y to 0 in the equation y = 2x - 6. This gives the equation 0 = 2x - 6. Solving for x, add 6 to both sides to get 6 = 2x, and then divide by 2, resulting in x = 3. Thus, the x-intercept is 3.

6. Solve the system: x + y = 7 and x - y = 3.

(5, 2)

(4, 3)

(6, 1)

(3, 4)

To solve the system of equations, substitute values from the answer choices into both equations. Testing (5, 2): x + y = 5 + 2 = 7 and x - y = 5 - 2 = 3, both equations are satisfied. Thus, (5, 2) is the solution to the system.

Explanation

To solve the system of equations, substitute values from the answer choices into both equations. Testing (5, 2): x + y = 5 + 2 = 7 and x - y = 5 - 2 = 3, both equations are satisfied. Thus, (5, 2) is the solution to the system.

7. Which inequality represents x ≥ -3?

A closed dot at -3 with arrow left

An open dot at -3 with arrow left

A closed dot at -3 with arrow right

An open dot at -3 with arrow right

A closed dot at -3 indicates that -3 is included in the solution set, representing the inequality x ≥ -3. The arrow pointing right signifies that all values greater than -3 are also included, aligning with the concept of the inequality. This visual representation accurately reflects the range of values satisfying the inequality.

Explanation

A closed dot at -3 indicates that -3 is included in the solution set, representing the inequality x ≥ -3. The arrow pointing right signifies that all values greater than -3 are also included, aligning with the concept of the inequality. This visual representation accurately reflects the range of values satisfying the inequality.

8. Simplify: 4(x - 2) + 3x = 20.

X = 4

X = 3

X = 5

X = 2

To simplify the equation 4(x - 2) + 3x = 20, first distribute the 4 to get 4x - 8 + 3x = 20. Combine like terms to obtain 7x - 8 = 20. Adding 8 to both sides results in 7x = 28, and dividing by 7 gives x = 4.

Explanation

To simplify the equation 4(x - 2) + 3x = 20, first distribute the 4 to get 4x - 8 + 3x = 20. Combine like terms to obtain 7x - 8 = 20. Adding 8 to both sides results in 7x = 28, and dividing by 7 gives x = 4.

9. The y-intercept of y = -3x + 5 is ____..

In the equation y = -3x + 5, the y-intercept is the value of y when x is 0. Substituting x = 0 into the equation gives y = -3(0) + 5, which simplifies to y = 5. Thus, the y-intercept is 5.

Explanation

In the equation y = -3x + 5, the y-intercept is the value of y when x is 0. Substituting x = 0 into the equation gives y = -3(0) + 5, which simplifies to y = 5. Thus, the y-intercept is 5.

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10. Solve: |x - 4| = 6.

X = 10 or x = -2

X = 10 or x = 2

X = -10 or x = 2

X = 4 or x = 6

To solve the equation |x - 4| = 6, we consider two cases: x - 4 = 6 and x - 4 = -6. Solving these gives x = 10 and x = -2, respectively. Therefore, the solutions to the equation are x = 10 and x = -2.

Explanation

To solve the equation |x - 4| = 6, we consider two cases: x - 4 = 6 and x - 4 = -6. Solving these gives x = 10 and x = -2, respectively. Therefore, the solutions to the equation are x = 10 and x = -2.

11. Which equation has slope -2 and y-intercept 3?

Y = -2x + 3

Y = 2x + 3

Y = 3x - 2

Y = -2x - 3

The equation y = -2x + 3 has a slope of -2, indicating that for every unit increase in x, y decreases by 2 units. The y-intercept is 3, meaning the line crosses the y-axis at the point (0, 3). This matches the required characteristics of the slope and y-intercept.

Explanation

The equation y = -2x + 3 has a slope of -2, indicating that for every unit increase in x, y decreases by 2 units. The y-intercept is 3, meaning the line crosses the y-axis at the point (0, 3). This matches the required characteristics of the slope and y-intercept.

12. Solve: 5x - 2(x + 3) = 12.

X = 6

X = 5

X = 4

X = 8

To solve the equation 5x - 2(x + 3) = 12, first distribute the -2 to get 5x - 2x - 6 = 12. This simplifies to 3x - 6 = 12. Adding 6 to both sides gives 3x = 18, and dividing by 3 results in x = 6.

Explanation

To solve the equation 5x - 2(x + 3) = 12, first distribute the -2 to get 5x - 2x - 6 = 12. This simplifies to 3x - 6 = 12. Adding 6 to both sides gives 3x = 18, and dividing by 3 results in x = 6.