1) \( |6 m|=42 \) \( \begin{array}{ll}\text { 3) }|k-10|=3 & \text { 2) }|-6 x|=30 \\ \text { 5) }|7+p|=7 & \text { 4) }\left|\frac{x}{7}\right|=3 \\ \text { 7) } 7|n|=56 & \text { 6) }|-3 p|=15 \\ \text { 9) }-3|p|=-12 & \text { 8) } \frac{|m|}{5}=3 \\ \text { 3. } & \text { 10) }|m|+2=11\end{array} \)

Sure, let's solve each of the absolute value equations you've provided. We'll go through them one by one. ### 1) \( |6m| = 42 \) **Solution:** \[ |6m| = 42 \implies 6|m| = 42 \implies |m| = 7 \implies m = \pm 7 \] **Answer:** \( m = 7 \) or \( m = -7 \) --- ### 2) \( |-6x| = 30 \) **Solution:** \[ |-6x| = 30 \implies 6|x| = 30 \implies |x| = 5 \implies x = \pm 5 \] **Answer:** \( x = 5 \) or \( x = -5 \) --- ### 3) \( |k - 10| = 3 \) **Solution:** \[ |k - 10| = 3 \implies k - 10 = 3 \quad \text{or} \quad k - 10 = -3 \] \[ \implies k = 13 \quad \text{or} \quad k = 7 \] **Answer:** \( k = 13 \) or \( k = 7 \) --- ### 4) \( \left|\frac{x}{7}\right| = 3 \) **Solution:** \[ \left|\frac{x}{7}\right| = 3 \implies \frac{|x|}{7} = 3 \implies |x| = 21 \implies x = \pm 21 \] **Answer:** \( x = 21 \) or \( x = -21 \) --- ### 5) \( |7 + p| = 7 \) **Solution:** \[ |7 + p| = 7 \implies 7 + p = 7 \quad \text{or} \quad 7 + p = -7 \] \[ \implies p = 0 \quad \text{or} \quad p = -14 \] **Answer:** \( p = 0 \) or \( p = -14 \) --- ### 6) \( |-3p| = 15 \) **Solution:** \[ |-3p| = 15 \implies 3|p| = 15 \implies |p| = 5 \implies p = \pm 5 \] **Answer:** \( p = 5 \) or \( p = -5 \) --- ### 7) \( 7|n| = 56 \) **Solution:** \[ 7|n| = 56 \implies |n| = 8 \implies n = \pm 8 \] **Answer:** \( n = 8 \) or \( n = -8 \) --- ### 8) \( \frac{|m|}{5} = 3 \) **Solution:** \[ \frac{|m|}{5} = 3 \implies |m| = 15 \implies m = \pm 15 \] **Answer:** \( m = 15 \) or \( m = -15 \) --- ### 9) \( -3|p| = -12 \) **Solution:** \[ -3|p| = -12 \implies 3|p| = 12 \implies |p| = 4 \implies p = \pm 4 \] **Answer:** \( p = 4 \) or \( p = -4 \) --- ### 10) \( |m| + 2 = 11 \) **Solution:** \[ |m| + 2 = 11 \implies |m| = 9 \implies m = \pm 9 \] **Answer:** \( m = 9 \) or \( m = -9 \) --- If you have any further questions or need more explanations on any of these solutions, feel free to ask!