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Algebra 1 : How to write expressions and equations

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Example Questions

Example Question #1041 : Linear Equations

Write the expression: Sixteen less than a number squared.

Possible Answers:

x^2-16 $\displaystyle x^2-16$

16-x^2 $\displaystyle 16-x^2$

$\displaystyle (x^2-16)^2$

$\displaystyle (x-16)^2$

$\displaystyle (16-x)^2$

Correct answer:

x^2-16 $\displaystyle x^2-16$

Explanation:

Separate the sentence into parts.

A number squared: x^2 $\displaystyle x^2$

Sixteen less than a number squared: x^2-16 $\displaystyle x^2-16$

Note that the number 16 is subtract from x^2 $\displaystyle x^2$ if 16 is less than the number.

The answer is: x^2-16 $\displaystyle x^2-16$

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Example Question #1042 : Linear Equations

Write as a variable expression:

Nine multiplied by the sum of a number and two thirds.

Possible Answers:

$9 \left ( x+\frac{2}{3}\right )$ $\displaystyle 9 \left ( x+\frac{2}{3}\right )$

$9 x+\frac{2}{3}$ $\displaystyle 9 x+\frac{2}{3}$

$9 +\frac{2}{3} x$ $\displaystyle 9 +\frac{2}{3} x$

$\frac{9 +2x}{3}$ $\displaystyle \frac{9 +2x}{3}$

$\frac{9 \left ( x+2 \right )}{3}$ $\displaystyle \frac{9 \left ( x+2 \right )}{3}$

Correct answer:

$9 \left ( x+\frac{2}{3}\right )$ $\displaystyle 9 \left ( x+\frac{2}{3}\right )$

Explanation:

"The sum of a number and two thirds" is the result of adding $\displaystyle x$ and $\frac{2}{3}$ $\displaystyle \frac{2}{3}$:

$x+ \frac{2}{3}$ $\displaystyle x+ \frac{2}{3}$

Nine multiplied by this, remembering to use parentheses to override the precedence of multiplication, is:

$9 \left ( x+\frac{2}{3}\right )$ $\displaystyle 9 \left ( x+\frac{2}{3}\right )$

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Example Question #1043 : Linear Equations

Write as a variable expression:

Twenty added to the product of seven tenths and a number

Possible Answers:

$\frac{7x+20}{10}$ $\displaystyle \frac{7x+20}{10}$

$\frac{7(x+20)}{10}$ $\displaystyle \frac{7(x+20)}{10}$

$\frac{7}{10}(x+20)$ $\displaystyle \frac{7}{10}(x+20)$

$\frac{7}{10}x+20$ $\displaystyle \frac{7}{10}x+20$

$\frac{7}{10}+20 x$ $\displaystyle \frac{7}{10}+20 x$

Correct answer:

$\frac{7}{10}x+20$ $\displaystyle \frac{7}{10}x+20$

Explanation:

"The product of seven tenths and a number" is the result of multiplying $\frac{7}{10}$ $\displaystyle \frac{7}{10}$ and $\displaystyle x$:

$\frac{7}{10}x$ $\displaystyle \frac{7}{10}x$.

"Twenty added to" this is

$\frac{7}{10}x+20$ $\displaystyle \frac{7}{10}x+20$

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Example Question #131 : How To Write Expressions And Equations

Which of the following English-language expressions can be rewritten as the algebraic expression $\frac{2}{3} (x-7)$ $\displaystyle \frac{2}{3} (x-7)$ ?

Possible Answers:

Two thirds multiplied by the difference of a number and seven

The product of a number and seven, subtracted from two thirds

Two thirds subtracted from the product of a number and seven

Two thirds multiplied by the difference of seven and a number

None of the other responses is correct

Correct answer:

Two thirds multiplied by the difference of a number and seven

Explanation:

$\frac{2}{3} (x-7)$ $\displaystyle \frac{2}{3} (x-7)$ is two thirds multiplied by x-7 $\displaystyle x-7$, which is the difference of a number and seven. Putting this together, this expression is stated as:

"Two thirds multiplied by the difference of a number and seven"

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Example Question #1051 : Linear Equations

"If seven is multiplied by the sum of an unknown number and twelve, the result is four times that unknown number."

Rewrite the above statement as a variable equation.

Possible Answers:

$\displaystyle 12(x+7) = 4x$

$\displaystyle 7x = 4x + 12$

$\displaystyle 12x = 4x + 7$

$\displaystyle 7(x+12) = 4x$

$\displaystyle 7x+12= 4x$

Correct answer:

$\displaystyle 7(x+12) = 4x$

Explanation:

If we call this unknown number $\displaystyle x$, then "the sum of an unknown number and twelve" is

x+12 $\displaystyle x+12$

"seven...multiplied by the sum of an unknown number and twelve" is seven multiplied by x+12 $\displaystyle x+12$; remembering to override the order of operations with parentheses, the expression is

7(x+12) $\displaystyle 7(x+12)$

The result is four times that unknown number, which is

$\displaystyle 4x$

Putting it together, the equation is

$\displaystyle 7(x+12) = 4x$

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Example Question #1052 : Linear Equations

Write the expression: One more than the quantity of twice a number squared.

Possible Answers:

$\displaystyle 2(x^2+1)$

$\displaystyle 2x(x+1)^2$

$\displaystyle 2(x+1)^2$

$\displaystyle (2x)^2+1$

2x^2+1 $\displaystyle 2x^2+1$

Correct answer:

$\displaystyle (2x)^2+1$

Explanation:

Split the sentence into parts. Let a variable be the number.

Twice a number: $\displaystyle 2x$

The quantity of twice a number squared: (2x)^2 $\displaystyle (2x)^2$

One more than the quantity of twice a number squared: $\displaystyle (2x)^2+1$

The answer is: $\displaystyle (2x)^2+1$

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Example Question #1053 : Linear Equations

Write the expression: Four less than half a number.

Possible Answers:

$\frac{1}{2}x-2$ $\displaystyle \frac{1}{2}x-2$

$\frac{1}{2}x-4$ $\displaystyle \frac{1}{2}x-4$

$4-\frac{1}{2}x$ $\displaystyle 4-\frac{1}{2}x$

$\frac{1}{2}(x-4)$ $\displaystyle \frac{1}{2}(x-4)$

$(4-\frac{1}{2})x$ $\displaystyle (4-\frac{1}{2})x$

Correct answer:

$\frac{1}{2}x-4$ $\displaystyle \frac{1}{2}x-4$

Explanation:

Separate the sentence into parts. Use a variable to denote the number.

Half a number: $\frac{1}{2}x$ $\displaystyle \frac{1}{2}x$

Four less than half a number: $\frac{1}{2}x-4$ $\displaystyle \frac{1}{2}x-4$

The answer is: $\frac{1}{2}x-4$ $\displaystyle \frac{1}{2}x-4$

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Example Question #1054 : Linear Equations

Write the following equation: Five more than twice a number is nine.

Possible Answers:

$\displaystyle (2+5)x=9$

$\displaystyle 2(x+5)=9$

2x=5+9 $\displaystyle 2x=5+9$

x+10=9 $\displaystyle x+10=9$

2x+5=9 $\displaystyle 2x+5=9$

Correct answer:

2x+5=9 $\displaystyle 2x+5=9$

Explanation:

Separate the sentence into parts.

Twice a number: $\displaystyle 2x$

Five more than twice a number: 2x+5 $\displaystyle 2x+5$

Is nine: $\displaystyle =9$

Combine the parts.

The answer is: 2x+5=9 $\displaystyle 2x+5=9$

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Example Question #1055 : Linear Equations

Write the expression: Six more than the cube root of twice a number.

Possible Answers:

$2\sqrt[3]{x}+6$ $\displaystyle 2\sqrt[3]{x}+6$

$\sqrt[3]{2x+6}$ $\displaystyle \sqrt[3]{2x+6}$

$2\sqrt[3]{x+6}$ $\displaystyle 2\sqrt[3]{x+6}$

$\sqrt[3]{2x}+6$ $\displaystyle \sqrt[3]{2x}+6$

$2\sqrt[3]{2(x+6)}$ $\displaystyle 2\sqrt[3]{2(x+6)}$

Correct answer:

$\sqrt[3]{2x}+6$ $\displaystyle \sqrt[3]{2x}+6$

Explanation:

Seperate the sentence into parts.

Twice a number: $\displaystyle 2x$

The cube root of twice a number: $\sqrt[3]{2x}$ $\displaystyle \sqrt[3]{2x}$

Six more than the cube root of twice a number: $\sqrt[3]{2x}+6$ $\displaystyle \sqrt[3]{2x}+6$

The answer is: $\sqrt[3]{2x}+6$ $\displaystyle \sqrt[3]{2x}+6$

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Example Question #1056 : Linear Equations

"If the product of one-tenths and a number is subtracted from six, the result is seven more than that number."

Rewrite the above statement as a variable equation.

Possible Answers:

$\frac{1}{10}x -6 = x + 7$ $\displaystyle \frac{1}{10}x -6 = x + 7$

$\frac{1}{10}(x -6) = x + 7$ $\displaystyle \frac{1}{10}(x -6) = x + 7$

$6 - \frac{1}{10}x = x + 7$ $\displaystyle 6 - \frac{1}{10}x = x + 7$

$\frac{1}{10}(x -6) = 7x$ $\displaystyle \frac{1}{10}(x -6) = 7x$

$\frac{1}{10}x -6 = 7x$ $\displaystyle \frac{1}{10}x -6 = 7x$

Correct answer:

$6 - \frac{1}{10}x = x + 7$ $\displaystyle 6 - \frac{1}{10}x = x + 7$

Explanation:

If we call this unknown number $\displaystyle x$, then "the product of one-tenths and a number" is $\frac{1}{10}x$ $\displaystyle \frac{1}{10}x$.

"The product of one-tenths and a number...subtracted from six" is $\frac{1}{10}x$ $\displaystyle \frac{1}{10}x$ subtracted from six, or

$6 - \frac{1}{10}x$ $\displaystyle 6 - \frac{1}{10}x$.

This result is equal to seven more than that number, which is x+7 $\displaystyle x+7$, so the equation is

$6 - \frac{1}{10}x = x + 7$ $\displaystyle 6 - \frac{1}{10}x = x + 7$.

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Algebra 1 : How to write expressions and equations

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #1041 : Linear Equations

Example Question #1042 : Linear Equations

Example Question #1043 : Linear Equations

Example Question #131 : How To Write Expressions And Equations

Example Question #1051 : Linear Equations

Example Question #1052 : Linear Equations

Example Question #1053 : Linear Equations

Example Question #1054 : Linear Equations

Example Question #1055 : Linear Equations

Example Question #1056 : Linear Equations

All Algebra 1 Resources

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