1){4x-7<1 {2x-7<1 2){1-x<5 {3x+1<3

Let's solve the inequalities step by step. ### Inequalities 1: 1) \( 4x - 7 < 1 \) **Step 1:** Add 7 to both sides: \[ 4x < 1 + 7 \] \[ 4x < 8 \] **Step 2:** Divide both sides by 4: \[ x < 2 \] 2) \( 2x - 7 < 1 \) **Step 1:** Add 7 to both sides: \[ 2x < 1 + 7 \] \[ 2x < 8 \] **Step 2:** Divide both sides by 2: \[ x < 4 \] ### Summary for Inequalities 1: - From the first inequality: \( x < 2 \) - From the second inequality: \( x < 4 \) ### Inequalities 2: 1) \( 1 - x < 5 \) **Step 1:** Subtract 1 from both sides: \[ -x < 5 - 1 \] \[ -x < 4 \] **Step 2:** Multiply both sides by -1 (remember to flip the inequality): \[ x > -4 \] 2) \( 3x + 1 < 3 \) **Step 1:** Subtract 1 from both sides: \[ 3x < 3 - 1 \] \[ 3x < 2 \] **Step 2:** Divide both sides by 3: \[ x < \frac{2}{3} \] ### Summary for Inequalities 2: - From the first inequality: \( x > -4 \) - From the second inequality: \( x < \frac{2}{3} \) ### Final Results: 1) \( x < 2 \) and \( x < 4 \) implies \( x < 2 \) 2) \( -4 < x < \frac{2}{3} \) Feel free to ask if you need further explanations or assistance!