2023 HESI A2 MATH EXAM PREP Q&A

2023 HESI A2 MATH EXAM PREP Q&A 1. 1. QUESTION Solve for x: 5(4x + 3) – 4(2x + 1) = 47 o x = 3 o x = 36 o x = 20 o x = 12 x = 3 Step 1: Apply the distributive law The first step is to expand the terms 5(4x + 3) and 4(2x + 1) by distribution so 5(4x + 3) – 4(2x + 1) = 47 becomes 20x + 15 – 8x – 4 = 47. Step 2: Combine like terms We can then collect like terms in 20x + 15 – 8x – 4 = 47. 12x + 11 = 47 Step 3: Subtract 11 on both sides We then have to subtract 11 on both sides to isolate the term with x. 12x + 11 – 11 = 47 – 11 12x = 36 Step 4: Divide by 12 on both sides We then divide both sides of the equation by 12 to isolate x. (12x)/12 = 36/12 1x = 3 We can drop the 1 on the left-hand side to x = 3. x = 3 is the solution of the equation. 2. 2. QUESTION Solve for x: 4x² – 61 = 135 o x = -7 or 7 o x = 14 or -14 o x = 7 o x = 14 x = 7 or -7 Step 1: Add 61 on both sides The first step in solving this problem is to add 61 from both sides of the equation. 4x² – 61 + 61 = 135 + 61 You should then carry out the addition of the numbers on both sides of the equation. 4x² = 196 Step 2: Divide by 4 on both sides We then divide both sides of the equation by 4. (4 x²)/4 = 196/4 x² = 49 Step 3: Take the square root on both sides The final step is to take the square root on both sides to solve for x. x² = 49 √x² = √49 x = 7 0r -7 If you are asking WHY the -7 gets included as well, it’s because any negative