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Select the correct answer from each drop-down menu.

Consider the equation below:

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

The equation was solved using the following steps:
Step 1: \quad [tex]\(-10x - 16 = 14 + 6x\)[/tex]
Step 2: \quad [tex]\(-16x - 16 = 14\)[/tex]
Step 3: \quad [tex]\(-16x = 30\)[/tex]
Step 4: \quad [tex]\(x = \frac{30}{-16}\)[/tex]
Step 5: \quad [tex]\(x = -\frac{15}{8}\)[/tex]

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

[tex]\[
\begin{tabular}{l|}
Step 1: \text{Distribute } -2 \text{ to both terms inside the parentheses} \\
Step 2: \text{Combine like terms on both sides of the equation} \\
Step 3: \text{Add } 16x \text{ to both sides} \\
Step 4: \text{Divide both sides by } -16 \\
\end{tabular}
\][/tex]

Sagot :

GinnyAnswer
Sure, let's fill in the blanks for the steps and processes used to solve the equation:

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

Step 1: Distribute the -2 on the left-hand side.

Result: [tex]\(-10 x - 16 = 14 + 6 x\)[/tex]

Step 2: Move [tex]\( 6 x \)[/tex] to the left side and combine with [tex]\(-10 x\)[/tex], and move [tex]\(-16\)[/tex] to the right side by adding 16 to both sides.

Result: [tex]\(-16 x - 16 = 14 + 16\)[/tex]

Step 3: Simplify the right-hand side.

Result: [tex]\(-16 x = 30\)[/tex]

Step 4: Divide both sides by -16.

Result: [tex]\(x = \frac{30}{-16}\)[/tex]

So the completed statements are:

\begin{tabular}{l}
Step 1: Distribute the -2. \\
Step 2: Move [tex]\(6 x\)[/tex] to the left and add 16 to both sides. \\
Step 3: Simplify the right-hand side. \\
Step 4: Divide both sides by -16. \\
\end{tabular}

Thus, filling in the blanks in the statements:

The correct answers for the drop-down selections are:

\begin{tabular}{l}
Step 1: Distribute the -2. \\
Step 2: Move [tex]\(6 x\)[/tex] to the left and combine like terms, add 16 to both sides. \\
Step 3: Simplify the right-hand side. \\
Step 4: Divide both sides by -16. \\
\end{tabular}
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