Step StamperRulekeepers · expressions and properties

Stamps every step approved: the properties of equality, and the best first move.

Choosing a First Move

The properties of equality, and the best first move. In MathBound, the free Algebra I adventure game, Step Stamper asks these problems, and the only way past is to solve them.

Part of More topics: taught by some textbooks beyond the usual course.

Play this battle free

10 questions, no sign-up, nothing saved. Climbs from the basics to harder questions.

What you will practice

Which First Move?. Choose the most efficient first move for a linear equation: the number that clears every fraction, the operation to undo first, the term to move.

Worked examples

Made by the game’s own question engine. Try each one, then open its steps.

Example 1 · Which First Move?

Which

first

step

for

9 x + 14 = 8 x + 10

collects

the

x -terms

on

one

side

and

leaves

a

positive

coefficient

of

x ?

$Add$ $8 x$ $to$ $both$ $sides$
$Subtract$ $8 x$ $from$ $both$ $sides$
$Subtract$ $14$ $from$ $both$ $sides$
$Subtract$ $9 x$ $from$ $both$ $sides$

Show the worked steps

$Subtracting$ $the$ $smaller$ $x -term,$ $8 x,$ $moves$ $it$ $across$ $and$ $leaves$ $1 x$ $on$ $the$ $other$ $side.$
$Subtracting$ $9 x$ $would$ $also$ $collect$ $them,$ $but$ $with$ $the$ $coefficient$ $- 1 .$

Answer: $Subtract$ $8 x$ $from$ $both$ $sides$

Example 2 · Which First Move?

Which

first

step

for

4 (x + 9) = 48

leaves

the

fewest

steps

to

finish?

$Divide$ $both$ $sides$ $by$ $4$
$Multiply$ $both$ $sides$ $by$ $4$
$Subtract$ $9$ $from$ $both$ $sides$
$Distribute$ $the$ $4$

Show the worked steps

$48$ $is$ $a$ $multiple$ $of$ $4,$ $so$ $dividing$ $gives$ $x + 9 = 12,$ $and$ $one$ $more$ $step$ $gives$ $x = 3 .$
$Distributing$ $first$ $takes$ $three$ $steps:$ $4 x + 36 = 48,$ $then$ $4 x = 12,$ $then$ $x = 3 .$

Answer: $Divide$ $both$ $sides$ $by$ $4$

Example 3 · Which First Move?

Which

strategy

and

first

move

suit

\frac{x}{8} + \frac{x}{12} = 15 ?

$Rewriting:$ $add$ $the$ $fractions$ $to$ $get$ $\frac{2 x}{20} = 15$
$Fraction$ $Busters:$ $multiply$ $both$ $sides$ $by$ $24$
$Fraction$ $Busters:$ $multiply$ $both$ $sides$ $by$ $20$
$Undoing:$ $subtract$ $\frac{x}{12}$ $from$ $both$ $sides$

Show the worked steps

$Fractions$ $call$ $for$ $Fraction$ $Busters:$ $multiply$ $by$ $the$ $least$ $common$ $multiple$ $of$ $8$ $and$ $12, 24 .$
$That$ $gives$ $3 x + 2 x = 360,$ $with$ $no$ $fractions.$

Answer: $Fraction$ $Busters:$ $multiply$ $both$ $sides$ $by$ $24$

Where it is in your textbook

Textbook	Lessons
Open Up NC Math 1 (MVP)	7.8

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