These are advanced GED algebra problems. They combine many earlier skills — distributing, combining like terms, managing negatives, and inverse operations — into one organized process. Stay organized, work one step at a time, and use the calculator for the arithmetic.
This stage contains advanced algebra skills that build on earlier lessons. You should already feel comfortable solving 1-step and 2-step equations and inequalities before starting this page. These problems combine many earlier algebra skills together into one longer problem.
Master these earlier skills first, then come back here:
Do not get discouraged if these feel difficult at first. Many students can pass the GED before mastering these harder algebra problems. If a multistep problem is taking too long, it is completely okay to skip it and come back later. These are advanced GED algebra questions — treat them as a stretch goal, not a wall.
You already know every piece of these problems. You know how to distribute. You know how to combine like terms. You know how to use inverse operations to solve. A multistep equation just lines those skills up in order. The challenge is not hard arithmetic — it is staying organized and watching your signs. One step at a time.
The hard part is organizing the algebra, not the arithmetic. Use the calculator to reduce arithmetic mistakes, and put your energy into the setup, the signs, and the order of your steps. Sometimes the GED is testing organization more than algebra.
8 Things to Keep in Mind
Every problem on this page comes back to these eight ideas. You don't have to memorize them — just keep them nearby as you work.
1
Distribution may happen more than once. A problem can have a parenthesis on the left, the right, or both. Distribute each one carefully.
2
Combine like terms carefully. Keep variables with variables and constants with constants.
3
Negatives are the #1 source of mistakes. A dropped minus sign changes the whole answer. Write each sign out — don't do it in your head.
4
Inverse operations still solve it. Add/subtract to move constants, multiply/divide to free the variable — exactly like a 2-step equation, just with more steps.
5
Organization matters more than speed. Neat, stacked steps beat fast, messy ones every time.
6
Use the calculator for arithmetic. Let it handle the numbers so you can focus on signs and setup.
7
Inequalities sometimes need the sign flipped. If you multiply or divide by a negative number, flip the inequality sign.
8
Answer choices can sometimes be substituted. On multiple choice, plugging in the choices is sometimes faster than solving.
🎯 GED Strategy for Advanced Algebra Problems
Before any algebra, understand how these questions fit into the test. These questions can take longer than many other GED questions. That is normal — and it changes how you should play them.
Play the test smart
›You may already have enough to pass. Many students reach a passing score from easier questions before ever mastering these harder multistep problems. Bank the points you're good at first.
›Use your strongest skills first. Move through the test answering what's quick and comfortable, then circle back.
›It's okay to skip — temporarily. If a multistep problem is eating your time, flag it, move on, and come back later if time allows.
›Do not get stuck too long on one algebra problem. One hard question is worth the same as one easy one. Don't trade three easy points for one hard one.
Remember the goal. You're aiming to pass, not to ace every question. Move on and come back later if needed. These problems are a bonus, not a requirement.
🔁 The Backsolving Strategy (Plug In the Answers)
This is one of the most powerful GED strategies, and it deserves its own section. On multiple choice questions, the answer choices can help you. Sometimes plugging in the answers is faster than solving the whole equation. GED multiple choice questions can sometimes be worked backwards.
How backsolving works: the right answer is sitting right there in the choices. Instead of doing all the algebra, you can take each answer choice, substitute it in for the variable, and see which one makes the equation true. No distribution headaches, no sign mistakes — just careful arithmetic on the calculator.
Backsolving — Example A
Solve 3(x + 4) − 2(x − 1) = 15 Choices: A) x = 1 B) x = 5 C) x = 9 D) x = 13
→ Instead of distributing, test a choice. Try B, x = 5: 3(5 + 4) − 2(5 − 1) = 3(9) − 2(4) = 27 − 8 = 19. Too big (we need 15).
→ A smaller x makes the left side smaller. Try A, x = 1: 3(1 + 4) − 2(1 − 1) = 3(5) − 2(0) = 15 − 0 = 15. ✓
x = 1 — found by plugging in, no algebra needed.
Backsolving — Example B (start in the middle)
Solve 5(x − 2) + 8 = 23 Choices: A) x = 2 B) x = 5 C) x = 7 D) x = 9
→ Smart move: start with a middle choice. Try B, x = 5: 5(5 − 2) + 8 = 5(3) + 8 = 15 + 8 = 23. ✓ First try.
x = 5. Starting in the middle often saves a step — if it's too big or small, you know which way to go.
When to backsolve: it shines when the choices are simple numbers and the algebra looks messy. When the choices are expressions (like y = 2x + 1) or the equation is short, solving directly is usually faster. Keep both tools ready and pick whichever is quicker.
Distribution — One Piece at a Time
Distribution means multiplying the number outside the parentheses by every term inside. In a multistep problem you may distribute once, twice, or on both sides. Distribute carefully — this is where organized students pull ahead.
Color key: outside multiplier · variable terms · constant terms · watch this negative
One distribution
3(x + 4) = 3·x + 3·4 = 3x + 12
→ The 3 hits BOTH terms inside: the x and the 4.
Two distributions in one expression
3(x + 4) −2(x − 1)
→ Distribute the 3: 3x + 12. Then distribute the −2 (sign included!): −2·x + (−2)·(−1) = −2x + 2.
= 3x + 12 − 2x + 2
Negative outside the parentheses
−2(3x − 5) = (−2)·3x + (−2)·(−5) = −6x + 10
→ A negative outside flips the sign of every term inside. Notice −2 × −5 became positive 10.
The most common distribution mistake: forgetting the negative belongs to the whole parenthesis. The minus sign in front of "2(x − 1)" makes it −2 times each term — not just −2x. Carry that negative all the way through.
Combining Like Terms
After distributing, you'll often have several terms on one side. Combine them before solving. The rule is short: keep variables with variables, keep constants with constants.
Group x-terms together and number-terms together. 5x − 2x = 3x. 8 + 1 = 9.
Don't do this
Never combine a variable with a constant. 3x + 4 is NOT 7x. They are different kinds of terms and can't merge.
Subtraction slip
The sign in front of a term belongs to it. In 3x − 2x, that's +3 and −2, giving 1x — not 5x.
Lost-negative slip
12 − 2x + 2: the −2x stays negative. Combine only the constants (12 + 2 = 14); leave the −2x alone.
Multistep Inequalities & The Flip Rule
A multistep inequality is solved exactly like a multistep equation — distribute, combine, move variables, use inverse operations — with one extra rule you must never forget.
⚠️ The Extra Rule
If you multiply or divide both sides by a negative number, flip the inequality sign.
< becomes > · > becomes < · ≤ becomes ≥ · ≥ becomes ≤
This rule is the single most important thing on this page for inequalities, so here it is again: the sign flips ONLY when you multiply or divide by a negative number.
Flip — yes
Dividing by −3: −3x < 12 → x > −4. You divided by a negative, so < flipped to >.
Flip — no
Dividing by +3: 3x < 12 → x < 4. Positive divisor, so the sign stays the same.
Flip — no
Adding or subtracting never flips the sign. x − 5 > 2 → x > 7. Same direction.
Flip — no
Negatives in the problem don't matter — only the step you do. If you never multiply/divide by a negative, you never flip.
Be precise about this. The sign does not flip just because there are negative numbers in the problem, and it does not flip when you add or subtract. It flips only at the moment you multiply or divide both sides by a negative number.
Tap a button to test yourself.
The 5-Step Solving Routine
Whether it's an equation or an inequality, with parentheses on one side or both, the same five steps work every time. Learn this one routine and run it on every problem.
1
Distribute carefully on BOTH sides. Clear every parenthesis first, carrying negatives through.
2
Combine like terms on each side. Variables with variables, constants with constants.
3
Move the variables to one side. Add or subtract a variable term to gather all the x's together.
4
Move the constants to the other side. Add or subtract to get the numbers away from the variable.
5
Solve with inverse operations. Divide to free the variable — and if you divide by a negative in an inequality, flip the sign.
🔢 Worked Examples
Watch the same routine repeat in every example. The numbers change; the steps don't. Use the calculator for the arithmetic and keep your work stacked and neat.
→ Step 5 — Divide by +2 (positive!) → sign stays. No flip here, even though the problem had subtraction.
x > 3
The whole routine on one screen
1. Distribute every parenthesis (carry negatives through). 2. Combine like terms on each side. 3. Move variables to one side. 4. Move constants to the other. 5. Divide to solve — and if it's an inequality and you divided by a negative, flip the sign. Use the calculator throughout; spend your focus on signs and order.
🖩 Let the Calculator Do the Arithmetic
On the GED you have a calculator for most of the math test — use it. The hard part is organizing the algebra, not the numbers.
Use the calculator to reduce arithmetic mistakes. Focus your brain on the setup and the solving steps — the organization, the signs, the distribution, and the inverse operations. Put your energy into organization, signs, distribution, and inverse operations — not mental arithmetic. If a step needs 27 − 8 or 9 ÷ 11, type it in. There are no bonus points for doing it in your head.
⚠️ Common Mistakes
Almost every wrong answer on this skill comes from one of these. Knowing them in advance is half the battle — the Guided Practice bank includes "What mistake did the student make?" questions to train your eye.
Forgetting to distribute
3(x + 4) is 3x + 12, not 3x + 4. The number outside hits every term inside.
Distributing a negative wrong
−2(x − 1) = −2x + 2, not −2x − 2. A negative times a negative is positive.
Sign mistakes
A dropped minus sign changes everything. Write each sign out instead of tracking it in your head.
Combining unlike terms
3x + 4 ≠ 7x. Variables and constants are different terms and can't be merged.
Forgetting to flip the sign
Divide an inequality by a negative? You must flip <→>. This is the most-missed inequality step.
Flipping when you shouldn't
Don't flip for adding/subtracting, or just because a negative appears. Flip only for multiply/divide by a negative.
Steps out of order
Distribute and combine before moving terms across. Skipping ahead scrambles the signs.
Arithmetic slips
Most "algebra" errors are really arithmetic. Use the calculator to remove them.
Reference
GED Formula Sheet
A reminder of what's provided on test day — keep it handy while you practice.