Algebra and Functions – Basic 1

(6) Solve for \(x\):
\[ \frac{x}{4} – 3 = \frac{5}{2} \]

• (a) \( x = 12 \)
• (b) \( x = 4 \)
• (c) \( x = 14 \)
• (d) \( x = 10 \)

Answer

Correct Answer: (c) \( x = 14 \)

To solve for \(x\), isolate \(x\) on one side of the equation. Here’s the step-by-step solution: \frac{x}{4} - 3 = \frac{5}{2}

(7) Evaluate the expression:
\[ | -7 | + | -3 | \]

• (a) \( 10 \)
• (b) \( -10 \)
• (c) \( 10 \)
• (d) \( -10 \)

Answer

Correct Answer: (c) \( 10 \)

Evaluate the absolute values separately and then add them. Here’s the step-by-step solution: | -7 | + | -3 |

(8) If \( f(x) = 3x + 2 \) and \( g(x) = 2x – 5 \), find \( (f \circ g)(1) \) (i.e., \( f(g(1)) \)).

• (a) \( 0 \)
• (b) \( 4 \)
• (c) \( 6 \)
• (d) \( 7 \)

Answer

Correct Answer: (d) \( 7 \)

Find \( (f \circ g)(1) \) by first evaluating \( g(1) \) and then using this value in \( f(x) \). The detailed solution steps are: f(x) = 3x + 2, g(x) = 2x - 5, f(g(1))

(9) Solve for \(x\):
\[ 2(x – 3) = 5x – 7 \]

• (a) \( x = 3 \)
• (b) \( x = 2 \)
• (c) \( x = 5 \)
• (d) \( x = 4 \)

Answer

Correct Answer: (c) \( x = 5 \)

To solve for \(x\), simplify and isolate \(x\) on one side of the equation. Here’s the step-by-step solution: 2(x - 3) = 5x - 7

(10) Evaluate the expression:
\[ \frac{6x^3 + 9x^2 – 15x}{3x} \]

• (a) \( 3x^2 + 3x – 5 \)
• (b) \( 2x^2 + 3x – 5 \)
• (c) \( 2x^2 + 3x – 4 \)
• (d) \( 3x^2 + 3x – 4 \)

Answer

Correct Answer: (b) \( 2x^2 + 3x – 5 \)

To evaluate the expression, simplify the terms and factor out \(x\). Here’s the step-by-step solution: \frac{6x^3 + 9x^2 - 15x}{3x}