How to Solve One Step Equations

How to Solve One Step Equations?

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An equation says that two expressions have the same value. To solve an equation, keep the two sides balanced while you isolate the variable.

How One-Step Equations Work

A one-step equation needs one inverse operation. Addition is undone by subtraction, subtraction is undone by addition, multiplication is undone by division, and division is undone by multiplication.

  • If a number is added to the variable, subtract that number from both sides.
  • If a number is subtracted from the variable, add that number to both sides.
  • If the variable is multiplied by a nonzero number, divide both sides by that number.
  • If the variable is divided by a nonzero number, multiply both sides by that number.

Examples

  • \(x-2=10\). Add 2 to both sides: \(x=10+2=12\).
  • \(x+7=-4\). Subtract 7 from both sides: \(x=-4-7=-11\).
  • \(6x=-30\). Divide both sides by 6: \(x=-5\).
  • \(\frac{x}{4}=9\). Multiply both sides by 4: \(x=36\).

One Step Equations

Think of this lesson as more than a rule to memorize. One Step Equations is about undoing operations while keeping both sides balanced. A strong student does not rush to the first formula on the page; they pause, identify the structure of the problem, and then choose the tool that matches that structure. That pause is what prevents most mistakes.

An equation is a balance. Whatever operation you use on one side, you must use on the other side so the two expressions stay equal.

Here is the teacher way to approach the topic. First, read the problem slowly and underline the information that is actually given. Next, name the target: are you finding a value, simplifying an expression, comparing two quantities, solving for a variable, or interpreting a graph? Once the target is clear, the calculation becomes much less mysterious because every step has a job.

  • Clear clutter such as parentheses or fractions.
  • Collect like terms.
  • Undo operations in reverse order.
  • Substitute the answer back or test a point.

A helpful habit is to say what each number represents before using it. For example, if a number is a denominator, a radius, a slope, a common difference, or a coefficient, it should not be treated like an ordinary loose number. Its role tells you where it belongs in the formula. This is especially important on ACT-style questions because many wrong answer choices come from using the right numbers in the wrong places.

Another good habit is to keep the work organized vertically. Write one clean line for substitution, one line for simplifying, and one line for the final answer. If the problem has units, keep the units attached. If the problem has signs, exponents, or parentheses, copy them carefully from one line to the next. Most errors in this topic are not caused by a hard idea; they are caused by dropping a negative sign, combining unlike terms, using the wrong denominator, or skipping a check.

When you finish, ask a quick reasonableness question. Should the answer be positive or negative? Should it be larger or smaller than the original number? Does it fit the graph, table, shape, or equation? Can you plug it back into the original problem? This final check turns the lesson from a procedure into understanding.

On a test, the goal is not to write the longest solution. The goal is to write enough clear work that you can see the structure, avoid traps, and recover quickly if one line goes wrong. Practice the examples below with that mindset: identify the type of problem, choose the matching rule, show the substitution, simplify carefully, and check the answer before moving on.

Free printable Worksheets

Exercises for One Step Equations

1) \( x + 7 = 15 \)\( \ \Rightarrow \ \)

2) \( x - 9 = 4 \)\( \ \Rightarrow \ \)

3) \( x + 12 = -3 \)\( \ \Rightarrow \ \)

4) \( x - 6 = -11 \)\( \ \Rightarrow \ \)

5) \( 4x = 28 \)\( \ \Rightarrow \ \)

6) \( -5x = 45 \)\( \ \Rightarrow \ \)

7) \( \frac{x}{3} = 8 \)\( \ \Rightarrow \ \)

8) \( \frac{x}{-4} = 6 \)\( \ \Rightarrow \ \)

9) \( x + \frac{5}{2} = 9 \)\( \ \Rightarrow \ \)

10) \( x - \frac{3}{4} = \frac{5}{8} \)\( \ \Rightarrow \ \)

11) \( 0.5x = 7 \)\( \ \Rightarrow \ \)

12) \( -\frac{2}{3}x = 10 \)\( \ \Rightarrow \ \)

13) \( x + (-8) = -20 \)\( \ \Rightarrow \ \)

14) \( x - (-6) = 17 \)\( \ \Rightarrow \ \)

15) \( \frac{x}{5} = -\frac{7}{2} \)\( \ \Rightarrow \ \)

16) \( -12 = x + 4 \)\( \ \Rightarrow \ \)

17) \( 18 = -3x \)\( \ \Rightarrow \ \)

18) \( \frac{3}{5}x = -9 \)\( \ \Rightarrow \ \)

19) \( x - 2.75 = 6.5 \)\( \ \Rightarrow \ \)

20) \( -\frac{x}{6} = \frac{11}{3} \)\( \ \Rightarrow \ \)

 
1) \( x + 7 = 15 \)
Subtract 7 from both sides: \(x+7-7=15-7\). So \(\color{red}{x=8}\).
2) \( x - 9 = 4 \)
Add 9 to both sides: \(x-9+9=4+9\). So \(\color{red}{x=13}\).
3) \( x + 12 = -3 \)
Subtract 12 from both sides: \(x+12-12=-3-12\). So \(\color{red}{x=-15}\).
4) \( x - 6 = -11 \)
Add 6 to both sides: \(x-6+6=-11+6\). So \(\color{red}{x=-5}\).
5) \( 4x = 28 \)
Divide both sides by 4: \(\frac{4x}{4}=\frac{28}{4}\). So \(\color{red}{x=7}\).
6) \( -5x = 45 \)
Divide both sides by -5: \(\frac{-5x}{-5}=\frac{45}{-5}\). So \(\color{red}{x=-9}\).
7) \( \frac{x}{3} = 8 \)
Multiply both sides by 3: \(3\cdot\frac{x}{3}=8\cdot3\). So \(\color{red}{x=24}\).
8) \( \frac{x}{-4} = 6 \)
Multiply both sides by -4: \((-4)\cdot\frac{x}{-4}=6(-4)\). So \(\color{red}{x=-24}\).
9) \( x + \frac{5}{2} = 9 \)
Subtract \(\frac{5}{2}\) from both sides: \(x=9-\frac{5}{2}=\frac{18}{2}-\frac{5}{2}\). So \(\color{red}{x=\frac{13}{2}}\).
10) \( x - \frac{3}{4} = \frac{5}{8} \)
Add \(\frac{3}{4}\) to both sides: \(x=\frac{5}{8}+\frac{3}{4}=\frac{5}{8}+\frac{6}{8}\). So \(\color{red}{x=\frac{11}{8}}\).
11) \( 0.5x = 7 \)
Divide both sides by 0.5: \(x=\frac{7}{0.5}\). Since \(0.5=\frac{1}{2}\), \(x=7\cdot2\). So \(\color{red}{x=14}\).
12) \( -\frac{2}{3}x = 10 \)
Multiply both sides by \(-\frac{3}{2}\): \(x=10\left(-\frac{3}{2}\right)\). So \(\color{red}{x=-15}\).
13) \( x + (-8) = -20 \)
Adding -8 means subtracting 8, so add 8 to both sides: \(x-8+8=-20+8\). So \(\color{red}{x=-12}\).
14) \( x - (-6) = 17 \)
Subtracting -6 means adding 6, so subtract 6 from both sides: \(x+6-6=17-6\). So \(\color{red}{x=11}\).
15) \( \frac{x}{5} = -\frac{7}{2} \)
Multiply both sides by 5: \(x=5\left(-\frac{7}{2}\right)\). So \(\color{red}{x=-\frac{35}{2}}\).
16) \( -12 = x + 4 \)
Subtract 4 from both sides: \(-12-4=x+4-4\). So \(\color{red}{x=-16}\).
17) \( 18 = -3x \)
Divide both sides by -3: \(\frac{18}{-3}=x\). So \(\color{red}{x=-6}\).
18) \( \frac{3}{5}x = -9 \)
Multiply both sides by the reciprocal \(\frac{5}{3}\): \(x=-9\cdot\frac{5}{3}\). So \(\color{red}{x=-15}\).
19) \( x - 2.75 = 6.5 \)
Add 2.75 to both sides: \(x=6.5+2.75\). So \(\color{red}{x=9.25}\).
20) \( -\frac{x}{6} = \frac{11}{3} \)
Multiply both sides by -6: \(x=\frac{11}{3}(-6)\). So \(\color{red}{x=-22}\).

One Step Equations Practice Quiz