Solve and graph \( -4<4-2 x \leq 10 \)

To solve the compound inequality \(-4 < 4 - 2x \leq 10\), we can split it into two parts and solve them separately. 1. For the first part, \(-4 < 4 - 2x\): \[ -4 < 4 - 2x \implies -4 - 4 < -2x \implies -8 < -2x \implies 4 > x \implies x < 4. \] 2. For the second part, \(4 - 2x \leq 10\): \[ 4 - 2x \leq 10 \implies -2x \leq 10 - 4 \implies -2x \leq 6 \implies x \geq -3. \] Putting the two parts together, we have: \[ -3 \leq x < 4. \] To graph this inequality on a number line, you would: - Draw an open circle at \(4\), indicating that \(4\) is not included. - Draw a closed circle at \(-3\), indicating that \(-3\) is included. - Shade the region between these points. This results in the range \([-3, 4)\) on the number line. Enjoy graphing!