# Algebra 1 : How to write expressions and equations

## Example Questions

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### Example Question #161 : How To Write Expressions And Equations

Write the expression:  Two times the difference of a number and forty.

Explanation:

Split up the sentence.

The difference of a number and forty:

Two times the difference of a number and forty:

The two will multiply the quantity of the difference.

### Example Question #162 : How To Write Expressions And Equations

Write the expression and simplify to the most reduced form:  The sum of square root two and square root three.

Explanation:

Write the values of square root two and square root three.

Square root two:

Square root three:

Sum these radicals.  Do not combine them as one whole!

### Example Question #163 : How To Write Expressions And Equations

Write the equation:  Eight less than a number squared is four.

Explanation:

Break up the sentence into parts.

A number squared:

Eight less than a number squared:

Is four:

Combine the parts to form the equation.

### Example Question #164 : How To Write Expressions And Equations

Write the equation: Half the quantity of a number less than four is nine.

Explanation:

Break up the sentence into parts.

A number less than four:

Half the quantity of a number less than four:

Is nine:

Combine the parts to form the equation.

### Example Question #165 : How To Write Expressions And Equations

Write the equation:  Fourteen more than thrice a number is fifteen.

Explanation:

Split up the sentence into parts.

Thrice a number:

Fourteen more than thrice a number:

Is fifteen:

Combine the terms to form an equation.

### Example Question #166 : How To Write Expressions And Equations

Write the equation:  Four times the quantity of four times a number is equal to six.

Explanation:

Break up the statement into parts.

Four times a number:

Four times the quantity of four times a number:

Is equal to six:

### Example Question #167 : How To Write Expressions And Equations

Write the equation:  Twelve more than six times the square of a number is negative four.

Explanation:

Break up the question in parts.

The square of a number:

Six times the square of a number:

Twelve more than six times the square of a number:

Is negative four:

Combine the terms to form an equation.

### Example Question #168 : How To Write Expressions And Equations

Write the equation:  Five less than six times a number is twelve.

Explanation:

Break up the sentence into parts.

Six times a number:

Five less than six times a number:

Is twelve:

Combine the parts to form an equation.

### Example Question #169 : How To Write Expressions And Equations

Write the expression:  Six less than twice a number.

Explanation:

To write the expression, split the sentence into parts.  An expression does not have an inequality or equal sign.

Twice a number:

Six less than twice a number:

### Example Question #161 : How To Write Expressions And Equations

Divide:

Answer must be in standard form.

Explanation:

Multiply both the numerator and the denominator by the conjugate of the denominator which is  resulting in

This is equal to

Since  you can make that substitution of  in place of  in both numerator and denominator, leaving:

When you then cancel the negatives in both numerator and denominator (remember that , simplifying each term), you're left with a denominator of  and a numerator of , which equals .

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