Question

justifying steps
match each step to its justification to solve $2x + 5 = 19$.
$2x/2 = 14/2$
$2x + 5 - 5 = 19 - 5$
$2x + 5 = 19$
$x = 7$
$2x = 14$
subtract
given
division property of equality
subtraction property of equality
divide

Explanation:

1. For the step \( \frac{2x}{2}=\frac{14}{2} \): This is using the division property of equality (dividing both sides by 2) or simply the action of dividing, so it matches with "division property of equality" or "divide". But more precisely, the division property of equality states that if \( a = b \), then \( \frac{a}{c}=\frac{b}{c} \) ( \( c

eq0 \) ), so this step is justified by the division property of equality.

1. For the step \( 2x + 5-5=19 - 5 \): This is using the subtraction property of equality (subtracting 5 from both sides), so it matches with "subtraction property of equality".
2. For the step \( 2x + 5=19 \): This is the original equation given to solve, so it matches with "given".
3. For the step \( x = 7 \): This is the result after dividing both sides of \( 2x=14 \) by 2, so the action here is dividing (or the result of the division property), so it matches with "divide" (or the result of the previous division step). Wait, actually, when we simplify \( \frac{2x}{2}=\frac{14}{2} \), we get \( x = 7 \), so the justification for \( x = 7 \) is the result of the division, so it's "divide" (the operation that leads to it).
4. For the step \( 2x=14 \): This is the result after subtracting 5 from both sides of \( 2x + 5=19 \), so the action here is subtracting (the result of the subtraction property), so it matches with "subtract" (the operation that leads to it).

Now, let's match each step correctly:

• \( \frac{2x}{2}=\frac{14}{2} \): division property of equality (because we divide both sides by 2, which is the division property of equality)
• \( 2x + 5-5=19 - 5 \): subtraction property of equality (because we subtract 5 from both sides, which is the subtraction property of equality)
• \( 2x + 5=19 \): given (it's the original equation)
• \( x = 7 \): divide (because we divide \( 2x \) by 2 and 14 by 2 to get \( x = 7 \))
• \( 2x=14 \): subtract (because we subtract 5 from both sides of \( 2x + 5=19 \) to get \( 2x=14 \))

So the correct matches are:

• \( \frac{2x}{2}=\frac{14}{2} \) → division property of equality
• \( 2x + 5-5=19 - 5 \) → subtraction property of equality
• \( 2x + 5=19 \) → given
• \( x = 7 \) → divide
• \( 2x=14 \) → subtract

Answer:

• \( \boldsymbol{\frac{2x}{2}=\frac{14}{2}} \) → division property of equality
• \( \boldsymbol{2x + 5-5=19 - 5} \) → subtraction property of equality
• \( \boldsymbol{2x + 5=19} \) → given
• \( \boldsymbol{x = 7} \) → divide
• \( \boldsymbol{2x=14} \) → subtract