Solving Equations
Solve for x: x + 9 = 15
x = 6
What is the slope of the line y = 3x + 5?
3
Simplify: √36
6
What two numbers multiply to 12 and add to 7?
3 and 4
Two lines intersect at (2, 3). What is the solution to the system?
(2, 3)
Which symbol means "less than or equal to"?
≤
Solve for x: 2x − 4 = 10
x = 7
What is the y-intercept of y = −2x + 7?
7
Simplify: x³ × x²
x⁵
Factor: x² + 5x
x(x + 5)
If two lines in a system are parallel, how many solutions does the system have?
Zero (no solution)
Solve: x + 4 > 10
x > 6
Solve for x: 3(x − 2) = 12
x = 6
What does a line with a slope of 0 look like?
A horizontal line
Simplify: (x⁴)²
x⁸
Factor: x² − 9
(x − 3)(x + 3)
True or False: A system where both equations describe the same line has infinitely many solutions.
True
If f(x) = x + 3, what is f(5)?
8
Solve for x: 5x + 3 = 2x + 18
x = 5
Find the slope between the points (1, 2) and (4, 11).
3
Simplify: x⁰ (where x ≠ 0)
1
Solve: x² = 25
x = 5 or x = −5
Solve the system: y = x + 1 and y = 5. What is x?
x = 4
True or False: Every function is a relation, but not every relation is a function.
True
What is the distributive property formula?
a(b + c) = ab + ac
What is the slope-intercept form of a linear equation?
y = mx + b
What is the rule for a negative exponent, x⁻ⁿ?
x⁻ⁿ = 1/xⁿ
What is the difference of squares formula?
a² − b² = (a − b)(a + b)
What is the standard form of a linear equation (commonly used for systems)?
Ax + By = C
What is the formula for the average rate of change of a function between x = a and x = b?
(f(b) − f(a)) / (b − a)
What is the quadratic formula?
x = (−b ± √(b² − 4ac)) / 2a
What is the point-slope form of a linear equation?
y − y₁ = m(x − x₁)
What is the rule for a rational (fraction) exponent, x^(m/n)?
ⁿ√(xm) (the nth root of x raised to the m)
What is the perfect square trinomial formula?
(a + b)² = a² + 2ab + b²
In slope-intercept form, what condition on the slopes and intercepts tells you a system has NO solution?
Same slope (m₁ = m₂), different y-intercepts (b₁ ≠ b₂)
What is the vertex formula for a quadratic in standard form ax² + bx + c?
x = −b / (2a)