This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here are the solutions to the inequalities: 1. Step 1: Distribute the -3 on the left side. 8m - 3(2m - 4) > 4 8m - 6m + 12 > 4 Step 2: Combine like terms. 2m + 12 > 4 Step 3: Subtract 12 from both sides. 2m > 4 - 12 2m > -8 Step 4: Divide by 2. m > (-8)/(2) m > -4 2. Step 1: Subtract 2 from both sides. 2 - (1)/(2)x < 5 -(1)/(2)x < 5 - 2 -(1)/(2)x < 3 Step 2: Multiply both sides by -2. Remember to reverse the inequality sign. x > 3 × (-2) x > -6 3. Step 1: Subtract 2 from both sides. 2 - ((x-1))/(3) 8 -((x-1))/(3) 8 - 2 -((x-1))/(3) 6 Step 2: Multiply both sides by -3. Remember to reverse the inequality sign. (x-1) 6 × (-3) x-1 -18 Step 3: Add 1 to both sides. x -18 + 1 x -17 4. Step 1: Multiply the entire inequality by the least common multiple of the denominators (2 and 3), which is 6. (1)/(2)(x-1) - (1)/(3)(x+5) < 1 6 × (1)/(2)(x-1) - 6 × (1)/(3)(x+5) < 6 × 1 3(x-1) - 2(x+5) < 6 Step 2: Distribute the 3 and the -2. 3x - 3 - 2x - 10 < 6 Step 3: Combine like terms. (3x - 2x) + (-3 - 10) < 6 x - 13 < 6 Step 4: Add 13 to both sides. x < 6 + 13 x < 19 5. Step 1: Multiply the entire inequality by the least common multiple of the denominators (3 and 6), which is 6. (2)/(3)(y-3) (5)/(6)(y+6) 6 × (2)/(3)(y-3) 6 × (5)/(6)(y+6) 2 × 2(y-3) 5(y+6) 4(y-3) 5(y+6) Step 2: Distribute the 4 and the 5. 4y - 12 5y + 30 Step 3: Subtract 4y from both sides. -12 5y - 4y + 30 -12 y + 30 Step 4: Subtract 30 from both sides. -12 - 30 y -42 y This can also be written as: y -42 Send me the next one 📸