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: Solve the inequality. First, distribute the (1)/(2) on the right side of the inequality. 7x + 4 < (1)/(2)(4x + 3) 7x + 4 < 2x + (3)/(2) Next, subtract 2x from both sides of the inequality. 7x - 2x + 4 < 2x - 2x + (3)/(2) 5x + 4 < (3)/(2) Now, subtract 4 from both sides. To do this, express 4 as a fraction with a denominator of 2, which is (8)/(2). 5x + 4 - 4 < (3)/(2) - 4 5x < (3)/(2) - (8)/(2) 5x < -(5)/(2) Finally, divide both sides by 5. x < (-5)/(2)5 x < -(5)/(2) × (1)/(5) x < -(1)/(2) Step 2: Illustrate the answer on a number line. The solution x < -(1)/(2) means all values of x that are strictly less than -(1)/(2). On a number line, this is represented by an open circle at -(1)/(2) (to indicate that -(1)/(2) is not included in the solution) and an arrow extending to the left from the open circle. 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