Question

step 1: subtract 3 from both sides of the inequality.
step 2: _______
step 3: divide both sides of the inequality by the coefficient of (x).

what is the missing step in solving the inequality (5 - 8x < 2x + 3)?

• subtract (8x) from both sides of the inequality.
• add (8x) to both sides of the inequality.
• add (2x) to both sides of the inequality.
• subtract (2x) from both sides of the inequality.

Explanation:

Analyze the given inequality and Step 1

Using the Solving Linear Inequalities knowledge point

$$ 5 - 8x < 2x + 3 $$

Subtracting 3 from both sides:

$$ 2 - 8x < 2x $$

Determine the missing Step 2

Using the Inequality Properties knowledge point
To isolate the variable terms on one side, we need to eliminate \(-8x\) from the left side.
Adding \(8x\) to both sides yields:

$$ 2 < 10x $$

Thus, the missing step is to add \(8x\) to both sides of the inequality.

Verify Step 3

Using the Solving Linear Inequalities knowledge point
Dividing both sides by the coefficient of \(x\) (which is 10):

$$ \frac{2}{10} < x \implies x > \frac{1}{5} $$

This matches the described sequence of steps perfectly.

Answer:

• Subtract \(8x\) from both sides of the inequality.
• Add \(8x\) to both sides of the inequality. (Correct answer)
• Add \(2x\) to both sides of the inequality.
• Subtract \(2x\) from both sides of the inequality.