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 for the given inequalities: *a) Solve -6 > 2x > 2 Step 1: Split the compound inequality into two separate inequalities. -6 > 2x and 2x > 2 Step 2: Solve each inequality for x. For the first inequality: (-6)/(2) > (2x)/(2) -3 > x For the second inequality: (2x)/(2) > (2)/(2) x > 1 Step 3: Combine the solutions. We need x < -3 and x > 1. There is no value of x that can be simultaneously less than -3 and greater than 1. The solution set is empty. No solution *b) Solve -12 < 3x < 6 Step 1: Divide all parts of the inequality by 3. (-12)/(3) < (3x)/(3) < (6)/(3) Step 2: Simplify the inequality. -4 < x < 2 *c) Solve -1 x+2 7 Step 1: Subtract 2 from all parts of the inequality. -1 - 2 x+2 - 2 7 - 2 Step 2: Simplify the inequality. -3 x 5 *d) Solve -5 < x-1 < 7 Step 1: Add 1 to all parts of the inequality. -5 + 1 < x-1 + 1 < 7 + 1 Step 2: Simplify the inequality. -4 < x < 8 *e) Solve -3 3x+3 9 Step 1: Subtract 3 from all parts of the inequality. -3 - 3 3x+3 - 3 9 - 3 -6 3x 6 Step 2: Divide all parts of the inequality by 3. (-6)/(3) (3x)/(3) (6)/(3) Step 3: Simplify the inequality. -2 x 2 *f) Solve -2 x-1 5 Step 1: Add 1 to all parts of the inequality. -2 + 1 x-1 + 1 5 + 1 Step 2: Simplify the inequality. -1 x 6 *g) Solve 2y+3 < 11 Step 1: Subtract 3 from both sides of the inequality. 2y+3 - 3 < 11 - 3 2y < 8 Step 2: Divide both sides by 2. (2y)/(2) < (8)/(2) Step 3: Simplify the inequality. y < 4 *h) Solve 2x-5 > 4x+7 Step 1: Subtract 2x from both sides of the inequality. 2x-5 - 2x > 4x+7 - 2x -5 > 2x+7 Step 2: Subtract 7 from both sides of the inequality. -5 - 7 > 2x+7 - 7 -12 > 2x Step 3: Divide both sides by 2. (-12)/(2) > (2x)/(2) Step 4: Simplify the inequality. -6 > x What's next? Send 'em! 📸