Question

practice & problem solving leveled practice in 6 and 7, fill in the boxes to solve each inequality. then graph the solutions. 6. $x + 5 < 7$ $x + 5 - \square \circ 7 - \square$ $x \circ \square$ (number line from -5 to 5) 7. $x - 4 \geq 12$ $x - 4 \circ \square \geq 12 \circ \square$ $x \geq \square$ (number line from 8 to 16)

Explanation:

Problem 6: Solve \( x + 5 < 7 \)

Step 1: Subtract 5 from both sides

To isolate \( x \), we use the subtraction property of inequality. Subtract 5 from both sides of the inequality \( x + 5 < 7 \). So we have \( x + 5 - 5 < 7 - 5 \).

Step 2: Simplify both sides

Simplifying the left side: \( x + 5 - 5 = x \). Simplifying the right side: \( 7 - 5 = 2 \). So the inequality becomes \( x < 2 \).

Step 1: Add 4 to both sides

To isolate \( x \), we use the addition property of inequality. Add 4 to both sides of the inequality \( x - 4 \geq 12 \). So we have \( x - 4 + 4 \geq 12 + 4 \).

Step 2: Simplify both sides

Simplifying the left side: \( x - 4 + 4 = x \). Simplifying the right side: \( 12 + 4 = 16 \). So the inequality becomes \( x \geq 16 \).

Answer:

For the boxes: First box: \( 5 \), Second box (the circle): \( < \), Third box: \( 5 \); Then the next circle: \( < \), and the last box: \( 2 \). So filled as \( x + 5 - \boldsymbol{5} \boldsymbol{<} 7 - \boldsymbol{5} \), \( x \boldsymbol{<} \boldsymbol{2} \).

Problem 7: Solve \( x - 4 \geq 12 \)