Interpreting Algebra Command Words and Notation

Hello! This first lesson begins the priority part of your test preparation: algebra language and notation. You already know some basic equation-solving, so the immediate goal is to make the English wording and symbols feel familiar rather than confusing.

By the end, you should be able to look at a question and identify what it is asking you to do, read its symbols aloud, and translate the most common algebra phrases into mathematical notation. We will use English terms with Hebrew translations throughout.

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The essential idea: read the mathematics before doing it

A math question has two “languages” at once:

1. Words tell you what action to take: solve, simplify, calculate, explain.
2. Notation shows the mathematical objects and relationships: $x$, $=$, $\frac{a}{b}$, $x^2$, and so on.

Do not rush to calculate. First ask:

• What is the command word?
• Is this an expression, an equation, or an inequality?
• What does each symbol mean?

For example:

$$3x+6=12$$

This is read: “three $x$ plus six equals twelve.”

It is an equation — משוואה — because it has an equals sign. If the question says solve the equation — פתור את המשוואה — you must find the value of $x$ that makes the two sides equal.

Notice an important point: the equals sign does not simply mean “the answer comes next.” It means:

The value on the left side is the same as the value on the right side.

So if $x=2$, then the left side of $3x+6=12$ becomes $3(2)+6=12$, which is true.

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Core algebra vocabulary: English and Hebrew

Keep this table nearby during the course. You do not need to memorize every term today; focus first on recognizing them.

English	Hebrew	Meaning
number	מספר	A value such as $7$, $-3$, or $\frac{1}{2}$
variable	משתנה	A letter standing for an unknown or changeable value, such as $x$
constant	קבוע	A fixed number, such as $6$ in $3x+6$
coefficient	מקדם	The number multiplying a variable, such as $3$ in $3x$
term	איבר	A part separated by addition or subtraction, such as $3x$ and $6$
expression	ביטוי אלגברי	A mathematical phrase with no equality statement, such as $4x-7$
equation	משוואה	A statement that two expressions are equal, such as $4x-7=9$
solution	פתרון	A value that makes an equation true
formula	נוסחה	A rule written with symbols, such as a formula for area
function	פונקציה	A rule connecting an input to an output
fraction	שבר	A number or algebraic expression written as a numerator over a denominator
numerator	מונה	The top of a fraction
denominator	מכנה	The bottom of a fraction
inequality	אי־שוויון	A comparison such as “greater than” or “less than”
domain	תחום ההגדרה	The permitted input values of a function or expression

A close look at one expression

Consider:

$$5x-8$$

• $x$ is the variable — משתנה.
• $5$ is the coefficient — מקדם.
• $5x$ is one term — איבר.
• $-8$ is another term and a constant — קבוע.
• The complete $5x-8$ is an expression — ביטוי אלגברי.

There is no equals sign, so it is not an equation yet.

Compare it with:

$$5x-8=12$$

Now it is an equation — משוואה — because it says that the expression $5x-8$ has the same value as $12$.

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Reading the most common symbols

Symbols save space, but they only help once you can read them confidently.

Symbol	Read in English	Hebrew	What it says
$+$	plus / added to	ועוד / פלוס	Add
$-$	minus / less	פחות	Subtract
$=$	equals / is equal to	שווה	The two sides have the same value
$\ne$	does not equal	לא שווה	The values are different
$>$	is greater than	גדול מ־	The left side is larger
$<$	is less than	קטן מ־	The left side is smaller
$\ge$	is greater than or equal to	גדול או שווה ל־	Greater, or exactly equal
$\le$	is less than or equal to	קטן או שווה ל־	Smaller, or exactly equal
$()$	parentheses / brackets	סוגריים	Group what must be handled together
$\frac{a}{b}$	$a$ divided by $b$	$a$ חלקי $b$	A fraction; $a$ is numerator, $b$ denominator
$x^2$	$x$ squared	$x$ בריבוע	$x$ multiplied by itself
$x^3$	$x$ cubed	$x$ בחזקה שלוש	$x\cdot x\cdot x$
$\sqrt{x}$	square root of $x$	שורש ריבועי של $x$	A number whose square is $x$

Two notation habits will help throughout the course:

Multiplication is often invisible

In algebra, multiplication is usually written without a multiplication sign:

$$3x=3\cdot x$$ $$2(x+4)=2\cdot (x+4)$$

So read $3x$ as “three $x$,” “three times $x$,” or “three multiplied by $x$.” Never read it as the number thirty-$x$.

Parentheses tell you what belongs together

Compare:

$$2x-6$$

with

$$2(x-6)$$

The first means: double $x$, then subtract $6$.

The second means: first calculate $x-6$, then double the entire result. The parentheses are meaningful; do not ignore them.

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Command words: what the question expects from you

Test questions often begin with one word. That word is not decoration; it tells you what kind of answer earns credit.

Command in English	Hebrew	What you should do
Find	מצא	Give the requested value, point, length, angle, or expression.
Calculate	חשב	Perform calculations and state the numerical result.
Solve	פתור	Find the value or values of the variable that make an equation true.
Simplify	פשט	Rewrite an expression in an equivalent, cleaner form.
Factor	פרק לגורמים	Rewrite an expression as multiplication.
Determine	קבע / מצא	Work out which value, type, condition, or set of values is correct.
Write	כתוב	Give the requested expression, equation, coordinates, or statement.
Explain	הסבר	Show reasoning, not only the final answer.
Show your steps	הראה / רשום את שלבי הפתרון	Write the important calculations in order.
Verify / Check	בדוק / וודא	Test whether an answer is correct, often by substitution.
Given	נתון	Information supplied in the question; use it.

Do not confuse these commands

Suppose you see:

$$4x+3-2x+5$$

• Simplify means combine or rewrite it more simply. You are not yet being asked for a value of $x$.
• Solve would require an equation, for example:

$$4x+3-2x+5=18$$

Now you must find the value of $x$ that makes the statement true.

Later lessons will teach the exact techniques for simplifying and solving. For now, the key is to recognize what each command demands.

“Explain” means show enough work to follow your thinking

For a written test, a final answer alone may not receive full credit. A clear answer usually has:

1. The equation or expression you used.
2. The important algebra steps.
3. The final answer, clearly marked.
4. A brief check when the question asks for one.

The exact rules for your placement test may be different, especially because you do not yet know whether it is written or multiple-choice. Still, showing organized steps is a safe habit whenever you have space.

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Translating English into algebra

When a question is written in words, build the mathematics in a controlled order.

1. Name the unknown.
   “A number” often becomes $x$.

2. Mark operation words.
   Words such as sum, difference, product, and quotient tell you which operation is happening.

3. Find the relationship word.
   Words such as is, equals, and gives often mean $=$.
   But be careful: in “is less than,” the relationship is $<$, not $=$.

4. Use parentheses when a whole group is being multiplied or divided.

Common operation language

English phrase	Mathematical meaning
a number increased by $5$	$x+5$
a number decreased by $5$	$x-5$
twice a number	$2x$
the product of $4$ and a number	$4x$
the sum of a number and $7$	$x+7$
the difference of a number and $7$	$x-7$
$7$ divided by a number	$\frac{7}{x}$
the quotient of a number and $3$	$\frac{x}{3}$
twice the difference of a number and $7$	$2(x-7)$

The final row is why parentheses matter. “Twice the difference” means multiply the entire difference by $2$.

The subtraction-order warning

Addition can be reversed without changing the result:

$$x+5=5+x$$

Subtraction cannot:

$$x-5\ne 5-x$$

Watch carefully for phrases that reverse the order.

English phrase	Correct translation	Reason
five less than a number	$x-5$	Begin with the number; remove $5$.
five subtracted from a number	$x-5$	$5$ is being removed from the number.
a number less $5$	$x-5$	Begin with the number, then subtract $5$.
a number is less than $5$	$x<5$	This compares two values; it is an inequality.

The words less than can therefore mean two different things depending on grammar:

• “Five less than a number” describes subtraction: $x-5$.
• “A number is less than five” describes a comparison: $x<5$.

When uncertain, say the sentence in a complete form: “What is being taken away from what?” That usually reveals the correct order.

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A short translation model

Read this statement:

“Five less than twice a number is $11$.”

Start with “a number,” so use $x$.

“Twice a number” is:

$$2x$$

“Five less than twice a number” means subtract $5$ from $2x$:

$$2x-5$$

“Is $11$” gives the equals sign:

$$2x-5=11$$

You do not need to solve it yet to understand the language. You have successfully translated English into an equation.

A useful habit for the next few days is to make a small two-column glossary in your notebook:

English	Hebrew / meaning
solve	פתור — find the value that makes an equation true
simplify	פשט — rewrite more simply but equivalently
coefficient	מקדם — number multiplying a variable
denominator	מכנה — bottom of a fraction
greater than	גדול מ־ — $>$

Add new words whenever you meet them. This turns unfamiliar English into a list you can steadily control.

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Key takeaways

• An expression — ביטוי אלגברי — has no equality claim; an equation — משוואה — uses $=$ to state that two values are equal.
• In $3x$, the $3$ is a coefficient — מקדם — and $x$ is a variable — משתנה.
• Read symbols precisely, especially $=$, $<$, $>$, fractions, parentheses, and exponents.
• Command words tell you what kind of answer is needed: solve, simplify, factor, calculate, determine, and explain are different tasks.
• Be especially careful with subtraction language: “five less than a number” is $x-5$, while “a number is less than five” is $x<5$.

Next, you will use this vocabulary to simplify algebraic expressions by combining like terms and applying the distributive property.