GED Mathematical reasoning 2 — Questions and Answers

Question 1: Solve for x: 3x − 7 = 14

x = 3
x = 5
x = 7 (Correct answer)
x = 9

Correct answer: x = 7

Add 7 to both sides: 3x = 21. Divide both sides by 3: x = 7.

To solve a linear equation, isolate the variable by performing inverse operations. Step 1: Add 7 to both sides to undo the subtraction. 3x − 7 + 7 = 14 + 7 3x = 21 Step 2: Divide both sides by 3 to undo the multiplication. 3x ÷ 3 = 21 ÷ 3 x = 7 Verification: substitute x = 7 back into the original equation: 3(7) − 7 = 21 − 7 = 14 ✓ Always verify your answer by substituting back into the original equation. This catches arithmetic errors and confirms your solution is correct.

Question 2: Which equation represents the line passing through (0, −3) with a slope of 2?

y = −3x + 2
y = 2x − 3 (Correct answer)
y = 2x + 3
y = −2x − 3

Correct answer: y = 2x − 3

Using slope-intercept form y = mx + b, slope m = 2 and y-intercept b = −3 gives y = 2x − 3.

The slope-intercept form of a linear equation is y = mx + b, where: • m = slope (rate of change) • b = y-intercept (where the line crosses the y-axis) Given information: • Slope (m) = 2 • The line passes through (0, −3), meaning the y-intercept (b) = −3 Substituting: y = 2x + (−3) = 2x − 3. You can verify by checking the point (0, −3): y = 2(0) − 3 = −3 ✓ The slope of 2 means for every 1 unit you move right, you move 2 units up. So another point on the line would be (1, −1): y = 2(1) − 3 = −1 ✓

Question 3: Simplify the expression: 4(2x − 3) + 5x

13x − 12 (Correct answer)
13x − 3
8x − 12 + 5x
13x + 12

Correct answer: 13x − 12

Distribute: 4(2x − 3) = 8x − 12. Then combine like terms: 8x + 5x − 12 = 13x − 12.

Simplifying algebraic expressions requires two key steps: distribution and combining like terms. Step 1 — Distribute 4 across (2x − 3): 4 × 2x = 8x 4 × (−3) = −12 So 4(2x − 3) = 8x − 12 Step 2 — Rewrite the full expression: 8x − 12 + 5x Step 3 — Combine like terms (terms with the same variable): 8x + 5x = 13x (x terms together) −12 stays (constant term) Result: 13x − 12 Note: Answer choice C shows the work halfway done but is not fully simplified. The GED expects fully simplified answers.

Question 4: A function is defined as f(x) = x² − 4x + 3. What is f(2)?

−1 (Correct answer)
0
3
7

Correct answer: −1

f(2) = (2)² − 4(2) + 3 = 4 − 8 + 3 = −1.

To evaluate a function at a specific value, substitute that value for x everywhere in the expression. f(x) = x² − 4x + 3 f(2) = (2)² − 4(2) + 3 Following order of operations: 1. Exponent: (2)² = 4 2. Multiplication: 4(2) = 8 3. Substituting: 4 − 8 + 3 4. Left to right: 4 − 8 = −4, then −4 + 3 = −1 f(2) = −1 Note that x = 2 is between the two roots of this quadratic. You can factor f(x) = (x−1)(x−3), which has roots at x = 1 and x = 3. At x = 2 (the midpoint), the parabola reaches its minimum value of −1.

Question 5: Solve the inequality: 2x + 5 > 13

x > 4 (Correct answer)
x > 9
x < 4
x ≥ 4

Correct answer: x > 4

Subtract 5: 2x > 8. Divide by 2: x > 4. The direction of the inequality does not change when dividing by a positive number.

Solving inequalities follows the same steps as solving equations, with one critical rule: if you multiply or divide both sides by a NEGATIVE number, you must flip the inequality sign. Step 1: Subtract 5 from both sides. 2x + 5 − 5 > 13 − 5 2x > 8 Step 2: Divide both sides by 2 (positive, so no flip). x > 4 This means any value greater than 4 (but NOT including 4) is a solution. On a number line, draw an open circle at 4 and shade to the right. Verification: Try x = 5: 2(5) + 5 = 15 > 13 ✓ Try x = 4: 2(4) + 5 = 13, which is NOT > 13 ✓ (4 is correctly excluded)

Question 6: If y varies directly with x, and y = 15 when x = 5, what is y when x = 8?

20
24 (Correct answer)
25
40

Correct answer: 24

Direct variation: y = kx. Find k: 15 = k(5), so k = 3. Then y = 3(8) = 24.

Direct variation means y = kx, where k is the constant of variation (also called the constant of proportionality). Step 1: Find k using the given values (y = 15, x = 5). y = kx → 15 = k(5) → k = 15/5 = 3 Step 2: Use k = 3 to find y when x = 8. y = 3(8) = 24 Alternatively, use proportions since y/x is constant: 15/5 = y/8 3 = y/8 y = 24 ✓ Direct variation graphs are straight lines through the origin (0, 0) with slope k. In this case, the line y = 3x passes through (0,0), (5,15), and (8,24).

GED Mathematical reasoning 2

Solve for x: 3x − 7 = 14