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Sagot :
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}
[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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