Chapter 2: Q1 (page 41)

Justify each step.
$\begin{matrix} 4 x - 5 = - 2 \\ 4 x = 3 \\ x = \frac{3}{4} \end{matrix}$

Short Answer

Expert verified

$4 x - 5 = - 2$ Given

$4 x = 3$ Addition property of equality

$x = \frac{3}{4}$ Division property of equality

Step by step solution

Step 1. Apply additional property of equality.

If $a = b$ and $c = d$ , then $a + c = b + d$ .

Step 2. Description of step.

Add 5 on both sides of $4 x - 5 = - 2$ and simplify.

$\begin{matrix} 4 x - 5 + 5 = - 2 + 5 \\ 4 x = 3 \end{matrix}$

Step 3. Apply the division property of equality.

If $a = b$ and $c \neq 0$ , then $\frac{a}{c} = \frac{b}{c}$ .

Step 4. Description of step.

Divide each side of the equation obtained in steps 2 by 4 to find the value of x.

$\begin{matrix} \frac{4 x}{4} = \frac{3}{4} \\ x = \frac{3}{4} \end{matrix}$

Therefore, the value of x is $\frac{3}{4}$ .

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Statement	Reasons
1. $\vec{B X}$ is the bisector of $∠ A B C$	1. ?
2. $∠ A B X ≅$ ?, or $m ∠ A B X =$ ?	2. ?
3. $m ∠ A B X + m ∠ X B C = m ∠ A B C$	3. ?
4. $m ∠ A B X + m ∠ A B X = m ∠ A B C$ , or $2 m ∠ A B X = m ∠ A B C$	4. ?
5. $m ∠ A B X = \frac{1}{2} m ∠ A B C$	5. ?
6. $m ∠ X B C = \frac{1}{2} m ∠ A B C$	6. Substitution Prop. (Steps ? and ?)

Justify each step.
$\begin{matrix} 4 x - 5 = - 2 \\ 4 x = 3 \\ x = \frac{3}{4} \end{matrix}$

Short Answer

Step by step solution

Step 1. Apply additional property of equality.

Step 2. Description of step.

Step 3. Apply the division property of equality.

Step 4. Description of step.

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Justify each step.4x−5=−24x=3x=34

Short Answer

Step by step solution

Step 1. Apply additional property of equality.

Step 2. Description of step.

Step 3. Apply the division property of equality.

Step 4. Description of step.

One App. One Place for Learning.

Most popular questions from this chapter

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Study anywhere. Anytime. Across all devices.

Justify each step.
$\begin{matrix} 4 x - 5 = - 2 \\ 4 x = 3 \\ x = \frac{3}{4} \end{matrix}$