University:
Jackson College
Course:
MAT-010 | Basic Mathematics
Academic year:

2024
Views:

55

Pages:

3
Author:

Bennett Wheeler

Question 1 Write each of the following in radical form. For example, 3 𝑥 2 3 = 3 𝑥 2 3 3x 3 2 =3 3 x 2 ( 2 𝑥 − 3 𝑦 ) 1 2 (2x−3y) 2 1 Answer 1 The general form to write the expression in radical form is: 𝑎 𝑚 𝑛 = 𝑎 𝑚 𝑛 a n m = n a m So, for ( 2 𝑥 − 3 𝑦 ) 1 2 (2x−3y) 2 1 , the radical form is: 2 𝑥 − 3 𝑦 2x−3y Question 2 Solve the exponential equation 3 𝑥 = 81 3 x =81 by expressing each side as a power of the same base and then equating exponents. Answer 1 Given: 3 𝑥 = 81 3 x =81 Rewrite 81 as a power of 3: 81 = 3 4 81=3 4 So we have: 3 𝑥 = 3 4 3 x =3 4 Since the bases are the same, equate the exponents: 𝑥 = 4 x=4 Thus, the solution is 𝑥 = 4 x=4. Question 3 Solve the equation 𝑚 − 4 = 2 𝑚 m−4=2m. Answer 1 Starting with: 𝑚 − 4 = 2 𝑚 m−4=2m Subtract 𝑚 m from both sides: − 4 = 𝑚 −4=m So, the solution is 𝑚 = − 4 m=−4. Question 4 What is the square root of 45? Answer 1 Notice that 45 can be rewritten as 9 × 5 9×5, where 9 is a perfect square. 45 = 9 × 5 = 9 × 5 = 3 5 45 = 9×5 = 9 × 5 =3 5 So, the square root of 45 in simplest radical form is 3 5 3 5 . For an approximate decimal form: 3 5 ≈ 6.708 3 5 ≈6.708 Question 5 Solve the equation. Write the solution sets to the inequalities in interval notation. ∣ 5 𝑥 − 1 ∣ = ∣ 3 − 4 𝑥 ∣ ∣5x−1∣=∣3−4x∣ Answer 1 Given: ∣ 5 𝑥 − 1 ∣ = ∣ 3 − 4 𝑥 ∣ ∣5x−1∣=∣3−4x∣ This absolute value equation splits into two cases: Case 1: 5 𝑥 − 1 = 3 − 4 𝑥 5x−1=3−4x Add 4 𝑥 4x to both sides: 9 𝑥 − 1 = 3 9x−1=3 Add 1 to both sides: 9 𝑥 = 4 9x=4 Divide by 9: 𝑥 = 4 9 x= 9 4 Case 2: 5 𝑥 − 1 = − ( 3 − 4 𝑥 ) 5x−1=−(3−4x) Distribute the negative: 5 𝑥 − 1 = − 3 + 4 𝑥 5x−1=−3+4x Subtract 4 𝑥 4x from both sides: 𝑥 − 1 = − 3 x−1=−3 Add 1 to both sides: 𝑥 = − 2 x=−2 So, the solutions are 𝑥 = 4 9 x= 9 4 and 𝑥 = − 2 x=−2.