Writing & Graphing
Write an inequality: "A number x is at least 7."
x ≥ 7
Solve: x + 9 > 14
x > 5
Solve: 2x + 3 < 11
x < 4
Solve: −2 < x + 3 < 5
−5 < x < 2
When you graph y > 2x + 1, is the boundary line solid or dashed?
Dashed, because the symbol is > with no "equal to."
When you graph x < −2 on a number line, do you use an open or closed circle, and which way do you shade?
Open circle at −2, shade left.
Solve: y − 6 ≤ −10
y ≤ −4
Solve: −4x + 1 ≥ 17
x ≤ −4
2x ≤ −6 OR x − 4 > 1
x ≤ −3 or x > 5
When you graph y ≤ −x + 4, do you shade above or below the line? Is the line solid or dashed?
Below, with a solid line.
A number line has a closed circle at 4 with shading to the left. Write the inequality.
x ≤ 4
Solve: 4n ≥ −28
n ≥ −7 (no flip, because you divided by a positive number)
Solve: 3(x − 2) > 12
x > 6
Solve: |x| < 4
−4 < x < 4
Is (2, 3) a solution to y < 3x − 2?
Yes. 3 < 3(2) − 2 simplifies to 3 < 4, which is true.
You must be at least 48 inches tall to ride a roller coaster. Write an inequality for height h.
h ≥ 48
Solve: −3x < 18
x > −6 (flip the sign, because you divided by a negative)
Solve: 5x − 7 ≤ 2x + 8
x ≤ 5
Solve: |x − 3| ≥ 5
x ≤ −2 or x ≥ 8
A graph has a dashed line with a y-intercept of −3 and a slope of 1/2, and it is shaded above the line. Write the inequality.
y > (1/2)x − 3
A phone plan costs $30 per month plus $0.10 per text. Jordan can spend no more than $45. Write AND solve an inequality for the number of texts, t.
30 + 0.10t ≤ 45, so t ≤ 150 texts
Solve: k ÷ (−5) ≥ 2. Then explain why the inequality sign changes.
k ≤ −10. Multiplying both sides by a negative number reverses the order of the numbers, so the sign has to flip to stay true.
Solve: 2(x + 4) > 2x + 5
All real numbers. The x's cancel and leave 8 > 5, which is always true.
Solve: 2|x + 1| − 3 < 7
−6 < x < 4. Isolate the absolute value first to get |x + 1| < 5.
Rewrite 4x − 2y < 8 in slope-intercept form, then describe the line and the shading.
y > 2x − 4. The line is dashed, with a y-intercept of −4 and a slope of 2, and you shade above. The sign flips when you divide by −2.