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Consider the equation below:

[tex]\[ -2(5x + 8) = 14 + 6x \][/tex]

The equation was solved using the following steps:

[tex]\[
\begin{array}{lrl}
\text{Step 1:} & -10x - 16 & = 14 + 6x \\
\text{Step 2:} & -16x - 16 & = 14 \\
\text{Step 3:} & -16x & = 30 \\
\text{Step 4:} & x & = \frac{30}{-16} \\
\text{Step 5:} & x & = -\frac{15}{8}
\end{array}
\][/tex]

Complete the statements below with the process used to achieve steps 1-4.

Step 1: Apply distributive property to [tex]\(-2\)[/tex] to [tex]\(5x\)[/tex] and [tex]\(8\)[/tex].

Step 2: Subtract [tex]\(6x\)[/tex] from both sides.

Step 3: Add [tex]\(16\)[/tex] to both sides.

Step 4: Divide by [tex]\(-16\)[/tex].

Sagot :

GinnyAnsweridn
Certainly! Let's go through the steps one by one to solve the equation [tex]\(-2(5x + 8) = 14 + 6x\)[/tex].

### Step 1:
Distribute the [tex]\(-2\)[/tex] to both [tex]\(5x\)[/tex] and [tex]\(8\)[/tex]. This means we multiply [tex]\(-2\)[/tex] by [tex]\(5x\)[/tex] and [tex]\(-2\)[/tex] by [tex]\(8\)[/tex]:

[tex]\[ -2(5x) + -2(8) = -10x - 16 \][/tex]

This gives us:

[tex]\[ -10x - 16 = 14 + 6x \][/tex]

So, for Step 1: Distribute [tex]\(-2\)[/tex] to [tex]\(5x\)[/tex] and [tex]\(8\)[/tex].

### Step 2:
Add [tex]\(10x\)[/tex] to both sides to combine like terms. This will move the [tex]\(10x\)[/tex] term to the right side:

[tex]\[ -10x - 16 + 10x = 14 + 6x + 10x \][/tex]

This simplifies to:

[tex]\[ -16 = 14 + 16x \][/tex]

So, for Step 2: Add [tex]\(10x\)[/tex] \to [tex]\(6x\)[/tex].

### Step 3:
Subtract 14 from both sides to isolate the terms with [tex]\(x\)[/tex]:

[tex]\[ -16 - 14 = 14 - 14 + 16x \][/tex]

This simplifies to:

[tex]\[ -30 = 16x \][/tex]

So, for Step 3: Subtract [tex]\(14\)[/tex].

### Step 4:
Divide both sides by [tex]\(-16\)[/tex] to solve for [tex]\(x\)[/tex]:

[tex]\[ \frac{-30}{16} = \frac{16x}{16} \][/tex]

This simplifies to:

[tex]\[ x = \frac{-30}{16} = -\frac{15}{8} \][/tex]

So, for Step 4: Divide by [tex]\(-16\)[/tex].

Putting it all together, the completed statements for steps 1-4 are:

Step 1: Distribute [tex]\(-2\)[/tex] to [tex]\(5x\)[/tex] and [tex]\(8\)[/tex].

Step 2: Add [tex]\(10x\)[/tex] to [tex]\(6x\)[/tex].

Step 3: Subtract [tex]\(14\)[/tex].

Step 4: Divide by [tex]\(-16\)[/tex].
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