5) Solve the inequality and graph the solutions. \( 5>12 a-(3-4 a) \)

To solve the inequality \( 5 > 12a - (3 - 4a) \) and graph the solution, follow these steps: ### Step 1: Simplify the Inequality Start by simplifying the right-hand side of the inequality. \[ 5 > 12a - (3 - 4a) \] Distribute the negative sign inside the parentheses: \[ 5 > 12a - 3 + 4a \] Combine like terms (\(12a + 4a\)): \[ 5 > 16a - 3 \] ### Step 2: Isolate the Variable Term Add 3 to both sides to move the constant term to the left side: \[ 5 + 3 > 16a \] \[ 8 > 16a \] ### Step 3: Solve for \( a \) Divide both sides by 16 to isolate \( a \): \[ \frac{8}{16} > a \] Simplify the fraction: \[ \frac{1}{2} > a \] This can also be written as: \[ a < \frac{1}{2} \] ### Step 4: Graph the Solution To graph the solution \( a < \frac{1}{2} \) on a number line: 1. **Draw a number line** with relevant points, including \( \frac{1}{2} \). 2. **Place an open circle** at \( \frac{1}{2} \) to indicate that \( \frac{1}{2} \) is **not** included in the solution (since the inequality is strictly "<"). 3. **Shade the region to the left** of \( \frac{1}{2} \) to represent all real numbers less than \( \frac{1}{2} \). Here is a visual representation: ``` <----|----------|----------|----------|----> 0 1/2 1 3/2 ●----------------> ``` - **●** represents the open circle at \( \frac{1}{2} \). - The arrow pointing to the left indicates all values less than \( \frac{1}{2} \). ### Final Answer All real numbers \( a \) less than \( \frac{1}{2} \). \[ a < \frac{1}{2} \] ### Graph of the Solution  *(In the graph, an open circle is placed at \( \frac{1}{2} \) with shading extending to the left.)*