3.07 One-step inequalities
Is a = 1 a solution of a + 9 \lt 12? Explain your answer.
Is y = 0 a solution of 12 - y \gt 10? Explain your answer.
Determine whether the following values satisfy the inequality x + 3 > 5:
x = 1
x = 3
x = - 9
x = 2
x = 5
x = 0
x = 12
x = -2
Solve:
x + 5 > 14
x + 5 \geq 11
9 > y + 4
n + 8 \leq 7
m - 5 > 9
7 \leq x - 3
x - 8 < 11
x - 8 \leq - 4
Solve:
10 x < 90
56 \leq 8 p
3 x \leq - 18
- 4 x < 32
- 4 y \geq - 16
- 5 x \leq - 40
- 24 < - 8 m
-3n \geq 30
Solve:
\dfrac{x}{3} \geq 6
\dfrac{n}{7} > 8
8 \geq \dfrac{x}{3}
\dfrac{a}{6} < 11
\dfrac{x}{- 9} \geq 5
\dfrac{x}{- 7} < 2
\dfrac{v}{- 3} \leq 3
\dfrac{m}{3} \geq -12
For each of the following:
Write the inequality described by the statement.
Solve for the value of x.
Seven more than the value of x is at least nine.
Half of x is no more than four.
Eight is greater than the result of taking seven away from x.
Negative eight multiplied by x is less than three.
For each of the following operations:
Write the new inequality.
State whether the new inequality still holds true.
Add 6 to both sides of the inequality 7 < 10.
Add 3 to both sides of the inequality 4 > - 2.
Subtract 5 from both sides of the inequality 1 < 3.
Subtract - \dfrac{1}{2} from both sides of the inequality \dfrac{3}{2} > \dfrac{1}{4}.
Multiply both sides of the inequality 5 < 7 by 2.
Divide both sides of the inequality 5 > 2 by 6.
Multiply both sides of the inequality -5 \leq 10 by -2.
Divide both sides of the inequality 24 \geq 18 by -3.
Given that a is a positive integer, determine whether the following operations maintain the inequality x\geq6:
Adding or subtracting a to both sides of the inequality.
Multiplying or dividing both sides of the inequality by a.
Multiplying or dividing both sides of the inequality by - a.
Adding or subtracting - a to both sides of the inequality.
Given that a is a negative integer, determine whether the following operations maintain the inequality x\leq2:
Adding or subtracting a to both sides of the inequality.
Multiplying or dividing both sides of the inequality by a.
Multiplying or dividing both sides of the inequality by - a.
Adding or subtracting - a to both sides of the inequality.
For each of the following:
Solve the inequality.
Graph the solution of the inequality on a number line.
x - 4 < 1
3 + x < 2
- 8 < x - 4
8 < 10 + x
- 5 + x < - 7
x - 2 \geq - 3
- 4 < - 3 + x
x + 2.5 \leq 7.5
x + 3.5 > 8
x - 2.6 \leq 2.4
- 4.5 + x \geq 4
x + \dfrac{7}{4} \geq \dfrac{9}{4}
6 x \leq 48
2 x > - 4
- 5 x \leq 15
- 3 x > - 21
72 > - 8 x
\dfrac{x}{2} \geq 7
\dfrac{x}{6} < - 2
\dfrac{x}{- 5} > 2
\dfrac{x}{- 7} < 2
- 2 \leq \dfrac{x}{- 7}
\dfrac{x}{3} > \dfrac{4}{3}
-4.5 x \geq -18