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Algebra: Equations Problems

The techniques for solving linear equations and linear inequalities are similar, yet different. Explain and give an example of both a linear equation and a linear inequality that demonstrates this difference.

1.) Solve and check the linear equation.

5x - 5 = 30
A) {30}
B) {34}
C) {11}
D) {7}

2.) Solve and check the linear equation.

9x - (7x - 1) = 2
A)
B)
C)
D)

3.) Solve and check the linear equation.

7x - 9 = -10 + 4x
A)
B)
C)
D)

4.) Solve and check the linear equation.

(-5x + 4) - 5 = -4(x - 7)
A) {19}
B) {- 6}
C) {29}
D) {- 29}

5.) Solve and check the linear equation.

-3x + 5 + 6(x + 1) = -2x + 3
A)
B)
C)
D)

6.) Solve and check the linear equation.

6[-6x + 6 + 4(x + 1)] = 6x + 2
A)
B)
C)
D)

7.) Solve and check the linear equation.

32 - 2(11 - 8)2 = 36x
A)
B) {4}
C)
D) {0}

8.) Solve and check the linear equation.

0.30(80) + 0.60x = 0.40(80 + x)
A) {20}
B) {30}
C) {50}
D) {40}

9.) Solve and check the linear equation.

0.40x - 0.20(50 + x) = -0.04(50)
A) {50}
B) {30}
C) {40}
D) {20}

10.) Solve the formula for the specified variable.

F = C + 32for C
A) C = (F - 32)
B) C =
C) C =
D) C = (F - 32)

11.) Solve the formula for the specified variable.

A = h(a + b)for a
A) a =
B) a =
C) a =
D) a =

12.) Solve the formula for the specified variable.

d = rtfor r
A) r = dt
B) r = d - t
C) r =
D) r =

13.) Solve the equation by factoring.

x2 = x + 6
A) {-2, -3}
B) {1, 6}
C) {-2, 3}
D) {2, 3}

14.) Solve the equation by factoring.

x2 + 2x - 120 = 0
A) {12, 10}
B) {12, -10}
C) {-12, 10}
D) {-12, 1}

15.) Solve the equation by factoring.

15x2 + 26x + 8 = 0
A)
B)
C)
D)

16.) Solve the equation by factoring.

2x2 - 15x = 8
A) {-2, 8}
B)
C)
D)

17.) Solve the equation by factoring.

11x2 - 9x = 0
A)
B)
C) {0}
D)

18.) Solve the equation by factoring.

3x(x - 5) = 7x2 - 16x
A)
B) {0}
C) {0, 4}
D)

19.) Solve the equation by factoring.

7 - 7x = (4x + 9)(x - 1)
A)
B) {-4, 1}
C)
D) {-1, 4}

20.) Solve the equation by factoring.

-6x - 2 = (3x + 1)2
A)
B)
C)
D)

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