Jul 21, 2024

- Focus on solving Algebra 1 questions easily.
- More detailed content available at ultimatealgebra.com.

- Goal: Isolate x on one side.
- Opposite operation of addition is subtraction.
- Steps:
- Subtract 2 from both sides: 5 - 2 = 3
- Result: x = 3

- Goal: Isolate x using reversal of the order of operations (PEMDAS).
- Steps:
- Subtract 3 from both sides: 11 - 3 = 8
- Divide both sides by 2: 8 / 2 = 4
- Result: x = 4

- Goal: Isolate x by using order of operations in reverse.
- Steps:
- Subtract 8 from both sides: 20 - 8 = 12
- Divide both sides by 3: 12 / 3 = 4
- Take the square root of both sides: √4 = 2
- Result: x = 2

- Goal: Move all x terms to one side.
- Steps:
- Subtract 2x from both sides: 4x - 2x = 2x
- Subtract 5 from both sides: 9 - 5 = 4
- Divide both sides by 2: 4 / 2 = 2
- Result: x = 2

- Goal: Consider positive and negative scenarios.
- Steps:
- x + 3 = 7 -> x = 4
- x + 3 = -7 -> x = -10
- Result: x = 4 or x = -10

- Goal: Isolate absolute value term.
- Steps:
- Subtract 6 from both sides: 9 - 6 = 3
- x + 1 = 3 -> x = 2
- x + 1 = -3 -> x = -4
- Result: x = 2 or x = -4

- Goal: Isolate the radical.
- Steps:
- Add 2 to both sides: 1 + 2 = 3
- Square both sides: 3^2 = 9
- Subtract 3 from both sides: 9 - 3 = 6
- Result: x = 6

- Goal: Cross-multiply to clear fractions.
- Steps:
- 4x = 3(x - 5) -> 4x = 3x - 15
- Subtract 3x from both sides: x = -15
- Result: x = -15

- Goal: Isolate x.
- Steps:
- Subtract b from both sides: y - b = mx
- Divide both sides by m: (y - b) / m = x
- Result: x = (y - b) / m

- Goal: Isolate x.
- Steps:
- Subtract 1 from both sides: 7 - 1 = 6
- Divide both sides by -3 -> flip inequality: 6 / -3 = -2
- Result: x < -2

- Goal: Isolate x.
- Steps:
- Subtract 8 from all sides: -11 < x < 12
- Result: -11 < x < 12

- Goal: Represent inequality on a number line.
- Steps:
- Locate the point -4.
- Draw an unshaded circle at -4.
- Draw arrow to the right.

- Total gallons = 2500, boxes = 20, leftover = 100
- Equation: 20x + 100 = 2500
- Steps:
- Subtract 100 from both sides: 2500 - 100 = 2400
- Divide by 20: 2400 / 20 = 120
- Result: 120 gallons per box

- Equation: 5 + 3x = 50
- Steps:
- Subtract 5 from both sides: 50 - 5 = 45
- Divide by 3: 45 / 3 = 15
- Result: Michael is 15 years old

- Function: No input value can have more than one output value.
- Example:
- (2 → 7), (2 → 5) is not a function.
- (4 → 8), (5 → 8) is a function.
- Answer: C (3 → 6, 3 → 8) is not a function.