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GED Algebra Practice: 25 Equation Questions, Solved Step by Step

An equation is a balance scale. Whatever you do to one side, you do to the other, and that one idea solves almost every equation on the GED. This page shows you how, one small step at a time.

Start 25 equations and inequalities questions

New questions every time you start. Come back as often as you like.

Updated September 25, 2026 · Lessons by Coach Crissy
Questions per set
25
Skills covered
10
Score-report category
Algebraic problem solving with expressions and equations · 30% of the test

Equations and inequalities: 25 questions

Questions
25
Timer
None
No calculator
None

New questions every time you start. Do this set as many times as you like.

  • Check each answer as you go and read the working before the next question.
  • The formula sheet and calculator sit in the toolbar, as they do on the real test.

No account or email needed.

If algebra is the point where math stopped making sense for you, you’re in good company.

Most GED equations are small money stories: a repair bill, a taxi fare, two gym plans. You already do this kind of math when you work out whether a deal is worth it. The letter x is just the number you don’t know yet.

The catch? The story comes in words, and turning it into an equation is half the work. The other half is one idea used over and over: keep the scale balanced.

On this page you’ll get:

  • 25 equation questions (scroll up), new ones every time
  • The one rule that solves most equations
  • Inequalities and quadratics, without the headache
  • The small slips that turn a right answer into a wrong one

Skills in this set: Solving two-step equations · Solving one-step equations · Solving equations with the variable on both sides · Solving equations with fractions or decimals · Solving a linear inequality · Writing and solving an equation from a situation · Solving a quadratic equation by factoring · Modeling a situation with a quadratic and solving it · Solving a system of two linear equations · Rearranging a formula to isolate a variable

What GED equation questions look like

Here’s the one rule. Picture a balance scale with both pans level. The equals sign says both sides weigh the same, so if you take 5 off one side, you take 5 off the other. Do that and the scale stays level every time.

Solving means undoing what was done to x, in reverse order. In 2x + 5 = 17, x was doubled and then 5 was added. So take 5 off both sides (2x = 12), then halve both sides (x = 6). Check it: 2 × 6 + 5 is 17.

The stories are about money and size: a repair bill with a call-out fee plus an hourly rate, two gym plans that cost the same after some number of visits, a patio 5 feet longer than it is wide. Ask what you pay once (the fee) and what you pay every time (the rate). The rate is the part that goes with the letter.

An inequality is an equation with a range for an answer. Think of the sign at a fairground ride: you must be at least this tall. Lots of heights pass, so the answer is “this number or more”. You solve it with the same balance moves, plus one twist you’ll see in the mistakes below, and you may be asked to show the answer on a number line.

A quadratic has an x² in it, and it usually has two answers. Think of a ball tossed in the air: it passes the same height twice, once going up and once coming down. To solve one, get zero on one side, then factor it or use the quadratic formula from the formula sheet. Graphing a quadratic and inequalities with two letters aren’t tested, according to a GED Testing Service board member’s presentation.

You’ll also see two equations solved together (like the gym plans) and formulas turned around to find a different letter, such as P = 2l + 2w solved for w. You might type the answer, drag the steps of a solution into order, or click a spot on a number line.

How many questions? GED Testing Service doesn’t publish a count per topic. Equations share the biggest scoring area, about 30% of the test, with expressions, so our estimate is six or seven equation questions out of about 46. A short one like 3(x − 2) = x + 8 could show up in the first five or so questions, where there’s no calculator, so try a few from the set by hand.

The topics and area weights come from GED Testing Service’s official test guide. It doesn’t publish a question count per topic, so any count here is our estimate.

The 4 mistakes that cost the most points

Each wrong answer in the practice set is the result of one specific slip, and the explanation names it. These are the ones that come up most in this topic.

1Forgetting to flip the sign when you divide by a negative

Solving −4x + 3 ≥ 15 goes like an equation until the last step: subtract 3 to get −4x ≥ 12, then divide by −4. Dividing or multiplying by a negative number flips the sign, so the answer is x ≤ −3. A thermometer shows why: 2 degrees is warmer than 1, but −2 is colder than −1. To check, try a number from your answer, such as −5: that gives 20 + 3 = 23, and 23 ≥ 15 is true.

2Stopping at one answer on a quadratic

(x − 5)(x + 2) = 0 is true when either set of parentheses equals zero, the way a string of lights goes dark if either of two switches is off. So x = 5 or x = −2. Wrong choices list only one of them, or list −5 and 2 with the signs left as they were. Keep both answers unless the story rules one out, like a negative width.

3Dividing only part of one side

To get w from P = 2l + 2w, subtract 2l, then divide everything that’s left by 2: w = (P − 2l) ÷ 2. It’s like splitting a dinner bill two ways, where the food and the tip both get split. Writing P ÷ 2 − 2l splits only the P. The quadratic formula has the same trap, because 2a divides the whole top line.

4Moving a term without changing its sign

In 5x + 7 = 2x − 8, subtract 2x from both sides and then subtract 7 from both sides. That gives 3x = −15, so x = −5. Say each step to yourself (“take 2x off both sides”), like lifting the same weight off each pan of the scale. Picturing terms hopping over the equals sign is where the minus sign usually gets lost.

One problem, worked out step by step

Worked example
Equations and inequalities

A climbing gym offers two ways to pay. The Basic plan costs $50 to set up and then $14 for each visit. The Flex plan costs $20 to set up and then $20 for each visit. After how many visits will the two plans have cost the same amount?

The working

  1. Write an expression for each plan
    Let v be the number of visits. Each setup fee is paid once and each per-visit price is paid v times, so the cost of a plan is its setup fee plus its rate times v.
    Basic: 50 + 14v; Flex: 20 + 20v
  2. Set the two costs equal
    The question asks when the plans cost the same, so the two expressions are equal at the number of visits you are looking for.
    50 + 14v = 20 + 20v
  3. Collect the v-terms on one side and the numbers on the other
    Subtract 14v from both sides so the variable appears only on the right, then subtract 20 from both sides so the plain number appears only on the left. Both moves keep the equation balanced.
    50 = 20 + 6v, so 30 = 6v
  4. Divide, then check in the original
    Dividing both sides by 6 gives v = 5. Substitute 5 back into both original expressions: the Basic plan costs 50 + 70 = 120 dollars and the Flex plan costs 20 + 100 = 120 dollars, so the answer holds.
    v = 30 ÷ 6 = 5; check: 50 + 14(5) = 120 and 20 + 20(5) = 120

Answer: 5 visits (both plans cost $120)

How to get better at this, fast

  1. On multiple choice, test the answers. Put each choice into the original equation and see which one makes both sides equal. For a quadratic, both numbers in the right choice have to work.
  2. Undo what was done to x in reverse order, the way you take off your shoes before your socks. In (x + 6) ÷ 3 = 4, x had 6 added and then was divided by 3, so multiply by 3 first and subtract 6 second: x = 6.
  3. Check every inequality with a test number. After you get x ≤ −3, put −5 into the original. If the result is false, a sign flip went wrong somewhere.
  4. For a quadratic, get zero on one side and write down a, b and c with their signs before anything else. Factor if you can. If you can’t, use the quadratic formula on the formula sheet.

Frequently asked questions

Is the quadratic formula on the GED formula sheet?

Yes, the sheet gives x = (−b ± √(b² − 4ac)) ÷ 2a. It won’t tell you which number is a, b or c, so practice on equations you can also factor and compare the two answers.

Does the GED care which method I use to solve an equation?

No. Only your answer is scored on the math test, so nobody sees your work. Use the method you trust, or try each answer choice in the equation.

Are systems of equations on the GED math test?

Yes. You may solve two equations together by graphing, substitution or elimination, often as two plans that cost the same after some months. When the answer is a point, watch for a choice with x and y swapped.

Do I have to graph inequalities on the GED?

Only on a number line, sometimes by clicking the right spot. Inequalities shaded on a grid aren’t tested, according to a GED Testing Service board member’s presentation.

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