Unit 4: Solving Linear Equations & Inequalities · NY-8.EE.7, AI-A.REI.3, AI-A.CED.1
Both exams
Notes
Balance, don't hop. Whatever you do to one side, do to the other. Distribute first, combine like terms, collect variable terms, then isolate.
Special cases. If you obtain 0 = 0, every real number works (identity). If you obtain 0 = 5, there is no solution. Algebra I also solves ax + b = c with letter coefficients.
Vocabulary
identity: An equation true for all values of the variable.
no solution: An equation that is never true.
Practice (no calculator unless marked)
The solution to 4(x − 5)/3 + 2 = 14 is
A. 15
B. 14
C. 6
D. 4
What value for the constant, k, will result in no solution for the equation k(5x + 7) = 10x + 12?
A. 5
B. 2
C. −2
D. −5
What value of x makes the equation 24x + 33 = 3(5x + 21) − 9 true?
The formula for the area of a trapezoid is A = ½(b₁ + b₂)h. The height, h, of the trapezoid may be expressed as
A. 2A − b₁ − b₂
B. 2A − b₁ / b₂
C. ½A − b₁ − b₂
D. 2A / (b₁ + b₂)
When solved for x in terms of a, the solution to the equation 3x − 7 = ax + 5 is
A. 12 / (3a)
B. 12 / (3 − a)
C. 3a / 12
D. (3 − a) / 12
The solution to 4(x − 5)/3 + 2 = 14 is
A. 15
B. 14
C. 6
D. 4
What value for the constant, k, will result in no solution for the equation k(5x + 7) = 10x + 12?
A. 5
B. 2
C. −2
D. −5
What value of x makes the equation 24x + 33 = 3(5x + 21) − 9 true?