Solve each equation for \( x \). Graph your solution on a number line. a. \( \quad 10-2(2 x+1)=4(x-2) \) b. \( \quad 5-(2 x-3)=-8+2 x \)

Let's solve each equation step-by-step and represent the solutions on a number line. --- ### Problem a. \[ 10 - 2(2x + 1) = 4(x - 2) \] **Step 1: Expand and simplify both sides.** \[ 10 - 4x - 2 = 4x - 8 \] \[ 8 - 4x = 4x - 8 \] **Step 2: Collect like terms.** \[ 8 + 8 = 4x + 4x \] \[ 16 = 8x \] **Step 3: Solve for \( x \).** \[ x = \frac{16}{8} = 2 \] **Solution:** \( x = 2 \) **Graph on a Number Line:** ``` <---|---|---|---|---|---> 0 1 2 3 4 ● ``` --- ### Problem b. \[ 5 - (2x - 3) = -8 + 2x \] **Step 1: Expand and simplify both sides.** \[ 5 - 2x + 3 = -8 + 2x \] \[ 8 - 2x = -8 + 2x \] **Step 2: Collect like terms.** \[ 8 + 8 = 2x + 2x \] \[ 16 = 4x \] **Step 3: Solve for \( x \).** \[ x = \frac{16}{4} = 4 \] **Solution:** \( x = 4 \) **Graph on a Number Line:** ``` <---|---|---|---|---|---|---> 0 1 2 3 4 5 ● ``` --- **Summary of Solutions:** - **a.** \( x = 2 \) - **b.** \( x = 4 \) Both solutions are represented on their respective number lines with a solid dot indicating the exact value of \( x \).