Solving Linear Equations Unit Test
100% please.
2. Solve for x. -6x = -42
3. Compare the solution of each equation to 0. Determine if the solution is less than 0, equal to 0, or greater than 0.
9x - 8 = -8
x/8 - 7 = -9
-24 = 6 + -3x
4. What is the first step when solving this equation?
2 (3x - 3) = 18
A. Add 3 to both sides.
B. Subtract 18 from both sides.
C. Divide by 3.
D. Distribute the 2.
5. Solve for x. 8 (2x + 3) = 40
6. Solve for x. -2(4x - 10) - 15 = -11
7. Liam is solving the equation 7x + 6 (x + 3) = 83. His steps are shown below. What mistake did Liam make while solving?
7x + 6 (x + 3) = 83
7x + 6x + 3 = 83
13x + 3 = 83
13x + 3 - 3 = 83 - 3
13x = 80
13x/13 = 80/13
x = 6 2/13
A. Liam should have added 3 to both sides of the equation rather than subtracting.
B. Liam should have subtracted 13 from both sides of the equation rather than dividing.
C. Liam did everything correctly.
D. Liam forgot to distribute the 6 to the 3.
8. Put the steps of solving the equation for x in order from the first step through finding the value of x.
4 - 2x = -5 (x + 7)
Put these steps in order options are:
3x/3 = -39/3
3x = -39
4 + 3x = -35
4 - 4 + 3x = -35 - 4
4 - 2x = -5x - 35
4 - 2x + 5x = -5x + 5x - 35
x = -13
9. Solve for x. 3x - 21 = 14 - 4x
10. Solve for x. 4 (1 + 3x) = 5 (x - 2)
11. How many solutions does the following equation have?
10x - 1 = 10x + 4
A. Infinitely many solutions.
B. One solution
C. Two solutions
D. no solutions
12. Which equation has exactly one solution?
A. 2x + 6 = 3x + 2
B. 9x + 3 = 9x - 9
C. 3 (x + 1) = 3x
D. 6x + 12 = 6 (x + 2)
13. Which is the solution to the equation below?
4x + 3 (x - 2) = 8x - (6 + x)
A. x = 6
B. infinite solutions
C. no solution
D. x = -4
14. Which equations have no solutions. Select all that apply.
A. 6 (x + 8) = 6x + 5
B. 2 (x + 2) = 2x + 2
C. 7x + 3 - 4x = 3 (x + 1)
D. 5x + 5 = 5 (2x + 2)
15. For each linear equation, indicate whether the equation has no solution, one solution. or infinitely many solutions.
6x + 2 - 4x = 2 (x - 2)
8 (x + 2) = 5x + 16 + 3x
3 (x + 3) = 7 + 3x - 6 - x
2. x = 7
3.
9x - 8 = -8
Solution: x = 0 (equal to 0)
x/8 - 7 = -9
Solution: x = -88 (less than 0)
-24 = 6 + -3x
Solution: x = -10 (less than 0)
4. D. Distribute the 2.
5. x = 2
6. x = 3
7. A. Liam should have added 3 to both sides of the equation rather than subtracting.
8.
4 - 2x = -5 (x + 7)
Steps in order:
-2x = -5x - 35
4 - 2x + 5x = -35
3x = -39
x = -13
9. x = 7
10. x = 3
11. D. no solutions
12. C. 3 (x + 1) = 3x
13. C. no solution
14. A and C
15.
6x + 2 - 4x = 2 (x - 2)
Solution: x = 2 (one solution)
8 (x + 2) = 5x + 16 + 3x
Solution: x = 2 (one solution)
3 (x + 3) = 7 + 3x - 6 - x
Solution: x = 2 (one solution)