Chapter 2: Q6 (page 41)

Justify each step.
$x - 2 = \frac{2 x + 8}{5}$
$5 (x - 2) = 2 x + 8$
$5 x - 10 = 2 x + 8$
$3 x - 10 = 8$
$3 x = 18$
$x = 6$

Short Answer

Expert verified

$x - 2 = \frac{2 x + 8}{5}$ Given

$5 (x - 2) = 2 x + 8$ Multiplication property of equality

$5 x - 10 = 2 x + 8$ distributive property

$3 x - 10 = 8$ Subtraction property of equality

$3 x = 18$ Addition property of equality

$x = 6$ Division property of equality

Step by step solution

Step 1. Apply the multiplication property of equality.

If $p = q$ then, $r p = r q$ .

Step 2. Description of step.

Multiply each side of the $x - 2 = \frac{2 x + 8}{5}$ by 5 and simplify.

$\begin{matrix} 5 \times (x - 2) = 5 \times \frac{2 x + 8}{5} \\ 5 (x - 2) = 2 x + 8 \end{matrix}$

Step 3. Apply the distributive property.

Expand the left-hand side of the equation obtained in step 2 using the distributive property.

$5 x - 10 = 2 x + 8$

Step 4. Apply the subtraction property of equality.

If $p = q$ and $r = s$ , then $p - r = q - s$ .

Step 5. Description of step.

Subtract $2 x$ from each side of the equation obtained in step 3 to find the value of x.

$5 x - 10 - 2 x = 2 x + 8 - 2 x$

$3 x - 10 = 8$

Step 6. Apply addition property of equality.

If $p = q$ and $r = s$ , then $p + r = q + s$ .

Step 7. Description of step.

Add 10 on each side of $3 x - 10 = 8$ and simplify.

$3 x - 10 + 10 = 8 + 10$

$3 x = 18$

Step 8. Apply the division property of equality.

Divide each side of the equation obtained in step 7 by 3 to find the value of x.

$\begin{matrix} \frac{3 x}{3} = \frac{18}{3} \\ x = 6 \end{matrix}$

Therefore, the value of x is 6.

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Justify each step.
$x - 2 = \frac{2 x + 8}{5}$
$5 (x - 2) = 2 x + 8$
$5 x - 10 = 2 x + 8$
$3 x - 10 = 8$
$3 x = 18$
$x = 6$

Short Answer

Step by step solution

Step 1. Apply the multiplication property of equality.

Step 2. Description of step.

Step 3. Apply the distributive property.

Step 4. Apply the subtraction property of equality.

Step 5. Description of step.

Step 6. Apply addition property of equality.

Step 7. Description of step.

Step 8. Apply the division property of equality.

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Justify each step.x−2=2x+855x−2=2x+85x−10=2x+83x−10=83x=18x=6

Short Answer

Step by step solution

Step 1. Apply the multiplication property of equality.

Step 2. Description of step.

Step 3. Apply the distributive property.

Step 4. Apply the subtraction property of equality.

Step 5. Description of step.

Step 6. Apply addition property of equality.

Step 7. Description of step.

Step 8. Apply the division property of equality.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Discrete Mathematics

Mechanics Maths

Theoretical and Mathematical Physics

Statistics

Calculus

Study anywhere. Anytime. Across all devices.

Justify each step.
$x - 2 = \frac{2 x + 8}{5}$
$5 (x - 2) = 2 x + 8$
$5 x - 10 = 2 x + 8$
$3 x - 10 = 8$
$3 x = 18$
$x = 6$