Question

solve for ( x ) and graph the solution on the number line below. if possible, resolve your answer to a single inequality. in case of no solution (( varnothing )), leave the number line blank.

( 17 < -x + 10 ) or ( 0 geq -x + 10 )

answer attempt 1 out of 2

inequality notation:

number line:
number line with -12, -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, 12, arrows left and right; touch and drag to plot line

submit answer

Explanation:

Step1: Solve \( 17 < -x + 10 \)

Subtract 10 from both sides: \( 17 - 10 < -x \) → \( 7 < -x \)
Multiply by -1 (reverse inequality): \( -7 > x \) or \( x < -7 \)

Step2: Solve \( 0 \geq -x + 10 \)

Subtract 10: \( -10 \geq -x \)
Multiply by -1 (reverse inequality): \( 10 \leq x \) or \( x \geq 10 \)

Step3: Combine solutions (or -statement)

The solutions are \( x < -7 \) or \( x \geq 10 \).

Answer:

Inequality Notation: \( x < -7 \) or \( x \geq 10 \)
(For the number line: Plot an open circle at -7, arrow left; closed circle at 10, arrow right.)