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
Let's solve these inequalities one by one. a) Solve the inequality (2x-3)/(5) (x)/(2) - 1 Step 1: Find a common denominator for all terms. The least common multiple of 5 and 2 is 10. Multiply every term by 10 to eliminate the denominators. 10 ((2x-3)/(5)) 10 ((x)/(2)) - 10(1) 2(2x-3) 5x - 10 Step 2: Distribute and simplify both sides of the inequality. 4x - 6 5x - 10 Step 3: Gather x terms on one side and constant terms on the other side. Subtract 4x from both sides. -6 5x - 4x - 10 -6 x - 10 Step 4: Add 10 to both sides to isolate x. -6 + 10 x 4 x This can also be written as x 4. x 4 b) Solve the inequality 4(x+1) < 2x + 3 Step 1: Distribute the 4 on the left side of the inequality. 4x + 4 < 2x + 3 Step 2: Gather x terms on one side and constant terms on the other. Subtract 2x from both sides. 4x - 2x + 4 < 3 2x + 4 < 3 Step 3: Subtract 4 from both sides to isolate the x term. 2x < 3 - 4 2x < -1 Step 4: Divide by 2 to solve for x. x < -(1)/(2) x < -(1)/(2) c) Solve the inequality -2(m-3) < 5(m+1) - 12 Step 1: Distribute the numbers on both sides of the inequality. -2m + 6 < 5m + 5 - 12 Step 2: Simplify the right side by combining constant terms. -2m + 6 < 5m - 7 Step 3: Gather m terms on one side and constant terms on the other. Add 2m to both sides. 6 < 5m + 2m - 7 6 < 7m - 7 Step 4: Add 7 to both sides to isolate the m term. 6 + 7 < 7m 13 < 7m Step 5: Divide by 7 to solve for m. (13)/(7) < m This can also be written as m > (13)/(7). m > (13)/(7) That's 2 down. 3 left today — send the next one.