Solving Equations with One Variable Worksheet

**Page 1**

1.

Solve : (6$x$^{2} + 9) (2$x$^{4} + 5) > 0

a. | (0 , ∞) only | ||

b. | (- ∞ , ∞) | ||

c. | (- ∞ , 0) only | ||

d. | Integers only |

(6

[

(2

[

So,

The solution of the inequality is (- ∞,∞).

Correct answer : (2)

2.

Which of the following are the solutions of the equation $\frac{3x}{x+5}+\frac{1}{x+2}$ = $\frac{7}{{x}^{2}+7x+10}$?

a. | $x$ = - 2.590 and 0.2573 | ||

b. | $x$ = 2 | ||

c. | $x$ = - 5.180 and 0.5146 | ||

d. | $x$ = - 7.2081 and 0.2081 |

3

[Multiply both sides of the equation by LCD

3

3

3

[Use quadratic formula.]

=

=

=

[Use a calculator.]

So, the solutions of the equation are -2.590 and 0.2573

Correct answer : (1)

3.

Solve the equation $\frac{x+5}{x}-\frac{7}{x+2}-\frac{26}{{x}^{2}+2x}$ = 0.

a. | $x$ = 4 | ||

b. | $x$ = ± 4 | ||

c. | $x$ = 16 | ||

d. | $x$ = ± 16 |

(

[Multiply both sides of the equation by the LCD (

So, the solution of the equation is

[The equation is not defined for

Correct answer : (1)

4.

Solve the equation $\frac{x+8}{x}-\frac{2}{x+2}$ = $\frac{1}{{x}^{2}+2x}$.

a. | $x$ = 5, - 3 | ||

b. | $x$ = 5, 3 | ||

c. | $x$ = - 5, - 3 | ||

d. | $x$ = - 5, 3 |

(

[Multiply both sides of the equation by the LCD

(

[Factor.]

So, the solutions of the given equation are - 5, - 3.

Correct answer : (3)

5.

Solve the equation $\frac{x-10}{11}$ + $\frac{x+12}{11}$ = $\frac{12}{11}$.

a. | $x$ = -5 | ||

b. | $x$ = 5 | ||

c. | $x$ = 10 | ||

d. | $x$ = -10 |

[Multiply both sides of the equation by the LCD 11 of the equation.]

2

2

Correct answer : (2)

6.

Which of the following are the solutions of the equation $x$ - $\frac{88}{x}$ = 3.

a. | $x$ = 0, 8 | ||

b. | $x$ = - 11, 8 | ||

c. | $x$ = - 8 , - 11 | ||

d. | $x$ = 11 , - 8 |

[Multiply both sides of the equation by the LCD

[Factor.]

(

So, the solutions of the equation are - 8 and 11

Correct answer : (4)

7.

Which of the following are the solutions of the equation $x$ + $\frac{9}{x-10}$ = 0?

a. | $x$ = 2 and - 18 | ||

b. | $x$ = 1 and - 9 | ||

c. | $x$ = 1 and 9 | ||

d. | $x$ = 2 and 18 |

[Multiply both sides of the eqation by the LCD

[Use Quadratic formula.]

=

=

Hence,

So, the solutions of the equation are

[Use a calculator.]

Correct answer : (3)

8.

Sum of a number and its reciprocal is - 2. Find the number.

a. | - 1 | ||

b. | - 2 | ||

c. | - 1, - 2 | ||

d. | $\frac{1}{2}$ |

[Multiply the equation by the LCD of the equation

(

So, the required number is - 1.

Correct answer : (1)

9.

Solve : $\frac{{x}^{2}}{x-7}$ < 0

a. | (- ∞ , 7) | ||

b. | (- ∞ , ∞) | ||

c. | [7 , ∞) | ||

d. | (7 , ∞) |

Since

If

If

So, the solution of the inequality is (7 , ∞).

Correct answer : (4)

10.

Solve ($x$ + 7)| $x$ - 5 | ≥ 0.

a. | (- 5, ∞] | ||

b. | [- 5, ∞) | ||

c. | (- 7, ∞] | ||

d. | [- 7, ∞) |

The factor |

The factor (

So, the solution of the given inequality is [- 7, ∞).

Correct answer : (4)