Expressions & equations worksheets – free PDFs, answer keys

Integers 3 skills

Absolute value Absolute value is a number's distance from zero, so it is never negative: |-8| and |8| both equal 8.
Comparing & ordering integers Picture the number line. The number farther to the right is always greater, so every positive beats every negative, and −2 beats −9.
Integers add & subtract Adding moves you right on the number line, subtracting moves you left, and subtracting a negative flips you right again.

Expressions & equations 33 skills

Adding linear expressions Remove the parentheses without changing signs. Combine like terms.
Checking contextual solutions Substitute into the original model. A solution must make it true and fit the quantity and its units.
Classifying linear solution sets Collect like terms on each side, then collect variable terms. A false constant equation means no solution; a true one means every real value is a solution.
Clearing fractional coefficients Multiply every term on both sides by a nonzero common multiple of the denominators.
Collecting rational like terms Add the coefficients of like terms. Use a common denominator to add fractions.
Collecting terms and constants Combine the variable terms and constants separately. Use common denominators for fractions.
Combining like terms Like terms have the same letter, so add their number parts: 3x + 2x makes 5x.
Equations in mixed numeric representations Choose fractions or exact decimals. Keep each value unchanged when converting.
Equations requiring collection of like terms Combine variable terms and constants separately on each side before solving.
Equations with infinitely many solutions Collect like terms on each side, then collect variable terms. A false constant equation means no solution; a true one means every real value is a solution.
Equations with no solution Collect like terms on each side, then collect variable terms. A false constant equation means no solution; a true one means every real value is a solution.
Evaluating expressions Swap the letter for its number, then follow the order of operations.
Expanding and collecting like terms Multiply each term inside the parentheses by the outside factor. Then combine like terms.
Expanding with rational factors Multiply each term inside the parentheses by the outside factor.
Exponents The small raised number tells how many times to use the base as a factor: 2^3 means 2 × 2 × 2.
Factoring out a specified rational factor Divide each term by the given factor. Keep that factor outside the parentheses, then expand to check.
Factoring out the greatest common factor Find the greatest positive integer that divides both coefficients. Factor it out, then expand to check.
Graphing inequality solution sets Use an open circle for < or > and a closed circle for ≤ or ≥. Shade toward the values that satisfy the inequality.
Inequalities on a number line The open circle marks the boundary number, and the arrow points toward all the numbers that make the inequality true.
One-step equations To find x, undo what was done to it: do the opposite operation to both sides.
Order of operations Work inside parentheses first, then any exponents, then multiply and divide, then add and subtract.
Solving equations with expansion on both sides Expand both groups. Collect variable terms on one side, isolate the variable.
Solving equations with one expansion Expand the parentheses first. Collect variable terms on one side, then isolate the variable. Check in the original equation.
Solving equations with variables on both sides Collect variable terms on one side, then isolate the variable. Check in the original equation.
Solving grouped equations Divide both sides by the factor outside the parentheses. Then undo the addition or subtraction.
Solving inequalities with negative coefficients Adding or subtracting preserves the direction. Dividing by a negative number reverses it.
Solving inequalities with positive coefficients Adding or subtracting preserves the direction. Dividing by a positive number also preserves it.
Solving two-step equations Undo the addition or subtraction first. Then divide both sides by the coefficient.
Subtracting grouped linear expressions Subtract every term in the second group, then combine like terms.
Writing equations from quantities Define the unknown and its units. Repeated quantity plus fixed amount equals the total.
Writing algebraic expressions Complete each problem. Show your reasoning where asked.
Writing inequalities Write one inequality that models each condition.
Writing numerical expressions Write each expression. Use grouping symbols where needed. Do not evaluate.