Question

solve the inequality and graph the solution on the line provided. -3x + 7 < 19
answer
attempt 1 out of 2
inequality notation:
number line:
-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12
touch and drag to plot line.
submit answer

Explanation:

Step1: Subtract 7 from both sides

To isolate the term with \( x \), we subtract 7 from both sides of the inequality \( -3x + 7 < 19 \). This gives us \( -3x + 7 - 7 < 19 - 7 \), which simplifies to \( -3x < 12 \).

Step2: Divide by -3 (and reverse inequality)

When dividing an inequality by a negative number, we reverse the inequality sign. Dividing both sides of \( -3x < 12 \) by -3, we get \( \frac{-3x}{-3} > \frac{12}{-3} \), which simplifies to \( x > -4 \).

Answer:

Inequality Notation: \( x > -4 \)
For the number line: Plot an open circle at -4 (since the inequality is strict, \( > \), not \( \geq \)) and draw an arrow to the right (indicating all numbers greater than -4).