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
Step 1: Simplify the first term and find the Least Common Multiple (LCM) of the denominators. The inequality is: (6x)/(3) - (5x-3)/(4) - (2x-1)/(6) > -(1)/(6) Simplify the first term: (6x)/(3) = 2x. The denominators are 3, 4, 6, and 6. The LCM of 3, 4, and 6 is 12. Step 2: Multiply every term in the inequality by the LCM (12) to eliminate the denominators. 12 ( 2x ) - 12 ( (5x-3)/(4) ) - 12 ( (2x-1)/(6) ) > 12 ( -(1)/(6) ) Step 3: Simplify each term. 24x - 3(5x-3) - 2(2x-1) > -2 Step 4: Distribute the numbers into the parentheses. Remember to distribute the negative signs. 24x - (15x - 9) - (4x - 2) > -2 24x - 15x + 9 - 4x + 2 > -2 Step 5: Combine like terms on the left side of the inequality. (24x - 15x - 4x) + (9 + 2) > -2 5x + 11 > -2 Step 6: Subtract 11 from both sides of the inequality. 5x > -2 - 11 5x > -13 Step 7: Divide both sides by 5 to solve for x. x > -(13)/(5) As a decimal, x > -2.6. Step 8: Represent the solution on a number line. Draw a number line. Place an open circle at -2.6 (since x is strictly greater than -2.6, not equal to it). Draw an arrow extending to the right from the open circle, indicating all values greater than -2.6. The solution is x > -(13)/(5). `mermaid graph TD A[Number Line] --> B(--- -3 --- -2.6 --- -2 --- -1 --- 0 ---); B --> COpen circle at -2.6; C --> D[Arrow pointing right from -2.6]; ` That's 2 down. 3 left today — send the next one.