HMH Algebra 1 ( Hacks)

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.