Question

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 (∅), leave the number line blank.
4 > -x + 6 or -x + 6 < 0
answer attempt 1 out of 2
inequality notation:
number line:
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Explanation:

Step1: Solve the first inequality \(4 > -x + 6\)

Subtract 6 from both sides: \(4 - 6 > -x + 6 - 6\)
Simplify: \(-2 > -x\)
Multiply both sides by -1 (reverse inequality): \(2 < x\) or \(x > 2\)

Step2: Solve the second inequality \(-x + 6 < 0\)

Subtract 6 from both sides: \(-x + 6 - 6 < 0 - 6\)
Simplify: \(-x < -6\)
Multiply both sides by -1 (reverse inequality): \(x > 6\)

Step3: Combine the solutions

We have \(x > 2\) or \(x > 6\). The union of these two sets is \(x > 2\) (since all \(x > 6\) are already included in \(x > 2\)).

Answer:

Inequality Notation: \(x > 2\) (or in interval notation \((2, \infty)\))

For the number line: Place an open circle at 2 and draw an arrow to the right.