1.
How to Solve Linear Equations
Steps:
1. Simplify both sides (remove parentheses, combine like terms).
2. Get all variables on one side, constants on the other.
3. Use inverse operations to isolate the variable (add/subtract first, then multiply/divide).
4. Check your answer by plugging it back into the original equation.
Example:
Solve 3x + 5 = 20
● Subtract 5 from both sides: 3x = 15
● Divide both sides by 3: x = 5
Practice:
a) 4x - 7 = 13
b) 2(x + 3) = 14
c) 5x/2 = 10
2.
How to Solve Inequalities
Steps:
Same as equations, but if you multiply or divide by a negative number, flip the inequality sign.
Example:
Solve -2x + 3 > 7
● Subtract 3: -2x > 4
, ● Divide by -2 (flip sign): x < -2
Practice:
a) 5x + 4 ≤ 19
b) -3(x - 2) ≥ 9
c) 2x - 5 < 7
3.
How to Graph Linear Equations
Steps:
1. Put the equation in slope-intercept form y = mx + b.
2. Plot the y-intercept (b) on the graph.
3. Use the slope (m = rise/run) to find the next points.
4. Draw a straight line through the points.
Practice:
Graph these:
a) y = 2x + 1
b) y = -1/2x + 3
c) y = 0.5x - 4
4.
How to Solve Systems of Equations by Substitution
Steps:
1. Solve one equation for one variable.
2. Substitute that expression into the other equation.
How to Solve Linear Equations
Steps:
1. Simplify both sides (remove parentheses, combine like terms).
2. Get all variables on one side, constants on the other.
3. Use inverse operations to isolate the variable (add/subtract first, then multiply/divide).
4. Check your answer by plugging it back into the original equation.
Example:
Solve 3x + 5 = 20
● Subtract 5 from both sides: 3x = 15
● Divide both sides by 3: x = 5
Practice:
a) 4x - 7 = 13
b) 2(x + 3) = 14
c) 5x/2 = 10
2.
How to Solve Inequalities
Steps:
Same as equations, but if you multiply or divide by a negative number, flip the inequality sign.
Example:
Solve -2x + 3 > 7
● Subtract 3: -2x > 4
, ● Divide by -2 (flip sign): x < -2
Practice:
a) 5x + 4 ≤ 19
b) -3(x - 2) ≥ 9
c) 2x - 5 < 7
3.
How to Graph Linear Equations
Steps:
1. Put the equation in slope-intercept form y = mx + b.
2. Plot the y-intercept (b) on the graph.
3. Use the slope (m = rise/run) to find the next points.
4. Draw a straight line through the points.
Practice:
Graph these:
a) y = 2x + 1
b) y = -1/2x + 3
c) y = 0.5x - 4
4.
How to Solve Systems of Equations by Substitution
Steps:
1. Solve one equation for one variable.
2. Substitute that expression into the other equation.
