Mod 6 top3solveand graph inequalities
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This document discusses solving and graphing linear inequalities with one variable. It provides examples of solving inequalities by adding or subtracting like terms and dividing by constants. When dividing an inequality by a negative number, the direction of the inequality symbol flips. The document also discusses graphing inequalities on a number line or coordinate plane. Closed inequalities with <= or >= are graphed as solid lines, while open inequalities with < or > are graphed as dashed lines. The region shaded depends on which side of the line the test point (0,0) falls in.
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This document contains 10 logic and sequence problems with solutions. The problems involve solving equations, identifying patterns in sequences, and working through definitions to find values. The solutions walk through applying the given operations or patterns to arrive at the answers in a step-by-step manner.
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This document contains 10 logic and sequence problems with solutions. The problems involve solving equations, identifying patterns in sequences, and working through definitions to find values. The solutions walk through step-by-step workings to arrive at the answers.
Linear functions
This document discusses how to graph a line from an equation. It provides the steps to plot the y-intercept, then rise by the slope and run right to plot additional points and connect them with a line with arrows at each end. The key pieces of information are the equation y=2/3x-4, the y-intercept is (0,-4), and the steps are to plot the y-intercept and then rise by the slope of 2/3 and run right 3 to plot additional points and draw the line.
Solving equations
This document discusses how to solve different types of equations: equations with one variable, more than one variable, and equations that can be written in the form of y = mx + b. It provides examples of solving equations with one variable by using the subtraction and division properties, and examples of solving equations for y in terms of x by isolating y and using the division property. Mastering these techniques is important for upcoming modules dealing with more advanced equation solving.
Linear functions
This document provides steps for graphing a line from an equation. It explains that the equation must be solved for y and defines the slope as "rise over run" and the y-intercept as b. The specific equation given is y=2/3x-4. It provides instructions to plot the y-intercept at (0,-4), then rise 2 and go right 3 to plot additional points and connect them with a line and arrows.
Combining like terms
The document defines exponents and provides examples of multiplying and combining like terms with exponents. It explains that to multiply terms, you multiply the coefficients and add the exponents of like terms. It provides examples of multiplying, combining, and dividing like terms with variables and exponents.
Combining like terms
The document defines exponents and provides examples of multiplying and combining like terms with exponents. It explains that to multiply terms, you multiply the coefficients and add the exponents of like terms. It provides examples of multiplying, combining, and dividing like terms with variables and exponents.
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Mod 6 top3solveand graph inequalities
- 1. Solve Inequalities with one variable and Graph linear inequalities
- 2. Solving Inequalities with 1 variable Basic Choices 2x – 3 ≤ -9 2(x-3) +4 < 5x +7 +3 +3 2x -6 +4 < 5x +7 2x ≤ -6 2x -2 < 5x +7 ***Choice x ≤ -3 Division by + 2 -5x -5x leaves the ≤ . -3x -2 < 7 -3x < 9 Solve just like an equation! x > -3 *** < flips > Why? Division by a neg
- 3. RULES When solving an inequality < > or ≤ ≥, follow the rules for solving an equation. IF DIVISION BY A NEGATIVE IS REQUIRERD, THE < BECOMES >! ONLY WHEN YOU DIVIDE (OR MULT) BY A NEGATIVE!
- 4. Graphing: y < mx + b Closed plane Open plane 2x + 3y ≥ 6 2x – 3y > 6 3y ≥ -2x +6 -3y > -2x +6 y ≥ -2/3x +2 y < 2/3x -2 Recall in y = mx + b < will NOT include the line, M = slope (rise over run) so it will be a dashed or B = y intercept dotted line! ≥ will include the line and will be graphed as a solid line
- 5. Completing the graph Open or closed plane: 1. < OR > is a dotted line 2. ≤ OR ≥ is a solid line SHADING After graphing the line, choose a point NOT ON THE LINE as a test point! I use (0,0) if possible!
- 6. Test previous examples slide # 4 y ≥ -2/3x +2 Line will be solid Test (0,0) 0 ≥ -2/3 (0) +2 0 ≥ 2 is false. SHADE THE SIDE THAT DOES NOT INCLUDE THE POINT (O,O) y < 2/3x -2 Line will be dotted Test 0 < 2/3(0) -2 0 < -2 is FALSE SHADE THE SIDE THAT DOES NOT INCLUDE THE POINT (O,O)
- 7. THE GRAPHS y ≥ -2/3x +2 y < 2/3x -2 Shade this side Shade this side