Review the following concepts if needed:

- Linear Inequalities Help
- Solving Linear Inequalities Help
- Linear Inequality Word Problems Help
- Double Inequalities Help

**Algebra Linear Inequalities Practice Test**

1. 2 *x* − 3 ≤ 7 + *x*

(a) *x* ≤ 10

(b) *x* > 10

(c) *x* ≤ –10

(d) *x* < 2

2. *x* < 5 is represented by

3. *x* ≥ – 6 is represented by

4. 4 *x* + 12 > 10 *x*

(a) *x* > 2

(b) *x* > – 2

(c) *x* < 2

(d) *x* < – 2

5. The interval notation for *x* > 1 is

(a) (– ∞,1)

(b) (1,∞)

(c) (– ∞, 1]

(d) [1, ∞)

6. A financial officer is splitting $500,000 between two bonds, one paying 6% interest and the other paying 8% interest (this bond carries more risk). A minimum of $36,500 of interest payments per year is required. How much can she spend on the 6% bond?

(a) She can spend at most $175,000 on the 6% bond.

(b) She can spend at least $175,000 on the 6% bond.

(c) She can spend at most $325,000 on the 6% bond.

(d) She can spend at least $325,000 on the 6% bond.

7. The interval notation for 3 < *x* ≤ 10 is

(a) (3, 10]

(b) [3, 10)

(c) [10, 3)

(d) (10, 3]

8. – < *x* < 6 is represented on the number line by

9. The interval notation for 8 ≤ *x* ≤ 2 is

(a) [8, 2]

(b) [2, 8]

(c) not an interval of numbers

10. –4 < 2 *x* −6 < 8

(a) – 4 < *x* < –2

(b) – 1 < *x* < 7

(c) – 2 < *x* < 4

(d) 1 < *x* < 7

11. The Martinez family budgets $60–85 for its monthly electric bill. The electric company charges a customer charge of $15 per month plus $0.08 per kilowatt-hour. What range of kilowatt-hours can they use each month to keep their electric bill in this range?

(a) At least 562.5 kilowatt-hours but no more than 875 kilowatthours

(b) More than 562.5 kilowatt-hours but less than 875 kilowatthours

(c) At least 750 kilowatt-hours but no more than 1062.5 kilowatt-hours

(d) More than 750 kilowatt-hours but less than 1062.5 kilowatt-hours

12. Joel wants to invest $10,000. Some will be deposited into an account earning 6% interest and the rest into an account earning interest. If he wants at least $650 interest each year, how much can he invest at ?

(a) At least $6000 at

(b) More than $6000 at

(c) At least $4000 at

(d) More than $4000 at

13. –2 < 4 –3 *x* < 2

(a) 2 < *x* < 4

(b) 10 < *x* < 20

(c) 7 < *x* < 17

(d) 8 < *x* < 18

15. The interval notation for *x* ≤ 6 is

(a) [–∞, 6]

(b) (–∞, 6)

(c) (–∞, 6]

(d) [–∞, 6)

**Solutions**

**1** . (a)

**2** . (c)

**3** . (b)

**4** . (c)

**5** . (b)

**6** . (a)

**7** . (a)

**8** . (c)

**9** . (c)

**10** . (d)

**11** . (a)

**12** . (c)

**13** . (b)

**14** . (d)

**15** . (c)

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