Ohio Algebra I: a complete guide to linear equations and inequalities

What this category demands

This guide covers linear equations and inequalities, the Ohio Algebra I block drawn from A-REI (reasoning with equations and inequalities), A-CED (creating equations), and the slope parts of F-IF. It is one of the largest, most reliable point blocks on the test, spanning the Expressions and Equations and Functions reporting categories, and much of it appears on the calculator-free Part 1. Each dot-point page has its own practice: solving linear equations, solving linear inequalities, literal equations and formulas, creating equations and inequalities, writing equations of lines, and slope and graphing lines.

Solving equations and inequalities

To solve a linear equation, clear parentheses and fractions, collect the variable on one side, and divide by the coefficient. If the variable cancels, a false statement means no solution and a true statement means infinitely many. To solve an inequality, do the same, but flip the inequality when you multiply or divide by a negative.

Rearranging formulas

A-CED.4 asks you to solve a formula for a chosen variable, treating the others as constants. The moves are the same inverse operations as numeric solving. Solving $A = \frac{1}{2}bh$ for $h$ gives $h = \frac{2A}{b}$; solving $V = \pi r^2 h$ for $r$ needs a square root: $r = \sqrt{\frac{V}{\pi h}}$. Equivalent exact forms are accepted.

Creating equations and inequalities

A-CED.1 is the modeling skill: define the variable, translate the words (a fixed amount is a constant, a rate is a coefficient), choose an equation (exact target) or an inequality (a limit), solve, and interpret.

Lines: writing and graphing

A-CED.2 and F-IF.6 cover lines. Both slope-intercept $y = mx + b$ and point-slope $y - y_1 = m(x - x_1)$ are on the reference sheet. From two points, find the slope $m = \frac{y_2 - y_1}{x_2 - x_1}$ first, then use point-slope. Parallel lines share a slope; perpendicular slopes are negative reciprocals. To graph from slope-intercept form, plot the $y$-intercept and step by the slope.

How this category is examined

• Equation and numeric entry. Solve an equation or inequality, rearrange a formula, or write a line's equation.
• Multiple choice and multiple-select. Count solutions, match an inequality to a number line, compute slope, or pick the equation from a graph.
• Graphing and drag and drop. Plot a line, place a number-line solution, or order solving steps.

Check your knowledge

Work these as you would for credit on the Ohio test.

1. Solve $4(x - 1) = 2x + 6$. (2 points)
2. How many solutions does $5x + 2 = 5x - 3$ have? (1 point)
3. Solve $-3x + 4 \geq 16$ and describe the number-line graph. (2 points)
4. Solve $d = rt$ for $r$. (1 point)
5. A club charges $10$ to join plus $4$ per event. Write an equation for cost $C$ after $n$ events, then find $n$ when $C = 38$. (2 points)
6. Write the line through $(1, 2)$ and $(3, -2)$ in slope-intercept form. (2 points)
7. Find both intercepts of $3x - 2y = 12$. (2 points)