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!