📐

Basic Algebra: Linear Equations & Inequalities

98 cards · 🇺🇸 English

Variables, expressions, linear equations and inequalities.

algebralinear-equationsinequalities

Study all 98 cards for free

Flashcards, quizzes, pixel-art games and a daily review that remembers for you.

Study this deck free

Try the first 10 cards

1 / 10

Question

Algebra

Knew itLearning

Tap the card for the answer · swipe right if you knew it, left if not

Already have an account? Sign in

Cards

1Algebra
A branch of mathematics that deals with abstract systems using variables and algebraic operations, generalizing arithmetic
2Variable in algebra
A symbol (usually a letter like x, y, or z) that represents an unspecified or unknown quantity
3Algebraic expression
A combination of variables, numbers, and arithmetic operations, such as 5x + 3 or 2y² - 4
4Equation
A mathematical statement that asserts two expressions are equal, using the equals sign (=), such as 3x + 5 = 14
5Inequality
A mathematical statement comparing two expressions using symbols like < (less than), > (greater than), ≤, or ≥
6Linear equation
An equation that can be written in the form ax + b = c, where a, b, and c are constants, and the variable appears only to the first power
7Goal of solving an equation
To find the value(s) of the variable(s) that make the equation true, usually by isolating the variable on one side
8Fundamental principle of equation solving
Whatever operation is applied to one side of an equation must also be applied to the other side to maintain balance
9for x: x + 7 = 15
x = 8. Subtract 7 from both sides: x + 7 - 7 = 15 - 7, so x = 8
10for y: 3y = 12
y = 4. Divide both sides by 3: 3y ÷ 3 = 12 ÷ 3, so y = 4
11Constant in algebra
A fixed value that does not change, typically represented by numbers or letters like a, b, c in general formulas
12Coefficient
A number that multiplies a variable, such as 5 in the expression 5x or -3 in -3y²
13Term in algebra
A single number, variable, or the product of numbers and variables, such as 7, x, or 4xy²
14Like terms
Terms that have the same variable(s) raised to the same power(s), such as 3x and 7x, which can be combined
15Combine like terms
Add or subtract their coefficients: 3x + 7x = 10x, or 8y - 3y = 5y
16Commutative property of addition
For any numbers a and b: a + b = b + a (the order doesn't matter)
17Distributive property
For any numbers a, b, and c: a(b + c) = ab + ac, allowing you to multiply a sum by distributing the multiplication
18Apply the distributive property: 3(x + 4)
3(x + 4) = 3x + 12
19Simplify: 2(3x - 5)
2(3x - 5) = 6x - 10
20Identity equation
An equation that is true for all values of the variable, such as x + 0 = x or 2(x + 3) = 2x + 6
21Conditional equation
An equation that is only true for specific values of the variable, such as x + 5 = 10 (only true when x = 5)
22for x: 2x - 6 = 10
x = 8. Add 6 to both sides: 2x = 16, then divide by 2: x = 8
23for a: 5a + 3 = 18
a = 3. Subtract 3 from both sides: 5a = 15, then divide by 5: a = 3
24Substitution in algebra
Replacing a variable with an equivalent expression or known value, such as if y = 2x + 1 and x = 3, then y = 2(3) + 1 = 7
25What does it mean to isolate a variable?
To manipulate an equation so the variable appears alone on one side, making its value clear (e.g., x = 5)
26for x: x/4 = 7
x = 28. Multiply both sides by 4: 4(x/4) = 4(7), so x = 28
27for y: -2y = 14
y = -7. Divide both sides by -2: y = 14 ÷ (-2) = -7
28Linear inequality
An inequality involving a linear expression, such as 2x + 3 < 10 or 5y - 2 ≥ 13
29Solve a linear inequality
Use the same operations as equations, but remember: when multiplying or dividing by a negative number, reverse the inequality sign
30Solve: x + 3 > 7
x > 4. Subtract 3 from both sides: x > 7 - 3, so x > 4