Algebra 1 Semester 1 Final Exam Flashcards

Inequalities

• Multiplying or dividing an inequality by a negative number necessitates flipping the inequality symbol.
• Closed circles on graphs indicate the inclusion of the endpoint, represented by having a line under the inequality symbol.

Functions and Graphing

• The domain of an ordered pair refers to the 'x' value, known as the independent value.
• The range of an ordered pair refers to the 'y' value, known as the dependent value.

Slope and Line Equations

• Slope formula: ( m = \frac{y_2 - y_1}{x_2 - x_1} ).
• Point-slope form: ( y - y_1 = m(x - x_1) ).
• Slope-intercept form: ( y = mx + b ).
• Standard form: ( Ax + By = C ).

Solving Equations

• Solutions to various equations include:
  • ( z + 4 = -3 ) results in ( z = -7 ).
  • ( \frac{y}{4} = -6 ) leads to ( y = -24 ).
  • ( -5x = -35 ) gives ( x = 7 ).
  • ( (w - 3) / -4 = 2 ) results in ( w = -5 ).
  • ( -18 = 9 - 3v ) leads to ( v = 9 ).
  • ( u / -3 + 6 = 14 ) results in ( u = -24 ).
  • ( 4t - 7 + 2 = -29 ) gives ( t = -6 ).
  • ( -5s - 9 + 8s = 36 ) results in ( s = 15 ).
  • ( 1 + 6r - 3 = 22 ) leads to ( r = 4 ).
  • ( 2(-q + 4) = -18 ) gives ( q = 13 ).
  • ( 3(p - 1) + 2p = 7 ) results in ( p = 2 ).
  • ( 1 - 3(3n + 1) = 25 ) leads to ( n = -3 ).
  • ( 4m + 3 = 3m + 10 ) results in ( m = 7 ).
  • ( 9l - 2 = 6l - 19 ) leads to ( l = -\frac{17}{3} ).

Word Problems

• Ariel spent $5.50 on a salad and had $27.70 left, indicating she started with $33.20.
• Wesley spent $10.25 on wings and sauces at Buffalo Wild Wings; he ordered 3 dipping sauces, given the base cost of wings and additional sauce charges.

Graphing Inequalities

• The inequality ( -2 > z ) is represented with an open circle at -2 and shading to the left.
• A closed circle at 1 shaded to the left is represented by the inequality ( x < 1 ).

Additional Equations

• The equation ( 5v + 6 - 3v ) simplifies to ( 2v + 6 ), highlighting the process of simplifying algebraic expressions.