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How do you solve a linear equation?
Isolate the variable by using opposite operations. Whatever you do to one side, you must do to the other.
What must you do when multiplying/dividing an inequality by a negative number?
Flip the inequality sign.
How do you check your solution to an equation?
Plug your solution back into the original equation to see if it holds true.
How do you represent the solution to $$x > 5$$ on a number line?
An open circle at 5 with an arrow pointing to the right.
How do you represent the solution to $$x \leq 2$$ on a number line?
A closed circle at 2 with an arrow pointing to the left.
When solving word problems, what should you always consider?
Context is key. Relate your mathematical answer back to the original problem. Units matter.
What does the solution to an inequality represent?
A range of values that satisfy the problem's conditions.
How do you determine if a solution is feasible?
Check if the solution makes sense in the real world (e.g., can't have negative time).
What is the first step in solving most linear equations?
Simplify both sides of the equation by distributing and combining like terms.
How do you handle a linear equation with fractions?
Multiply both sides of the equation by the least common multiple of the denominators to eliminate the fractions.
What is the form of a linear equation?
$$ax + b = c$$, where a, b, and c are real numbers and $$a ≠ 0$$.
What is the distributive property?
$$a(b+c) = ab + ac$$
What is the solution set of an inequality?
All values of 'x' that make the inequality true.
What do parentheses indicate in interval notation?
Strict inequalities ($$<$ or $$>$$). Example: $$(2, 5)$$
What do brackets indicate in interval notation?
Inclusive inequalities ($$\leq$$ or $$\geq$$). Example: $$[2, 5]$$
What is set-builder notation?
{x | condition}. Example: {x | x > 3}
What does an open circle on a number line represent?
Strict inequalities ($$<$ or $$>$$).
What does a closed circle on a number line represent?
Inclusive inequalities ($$\leq$$ or $$\geq$$).
What is an inconsistent equation?
An equation with no solution.
What is an identity equation?
An equation with infinitely many solutions.