Question

the following inequality has a solution in the form \\(x < a\\). solve the inequality and place the correct value of \\(a\\) into the box.

\\2(x - 7) - 1 < -1x + 3\\

answer: \\(x <\\)

enter your answer as an integer or a reduced fraction in the form a/b.

Explanation:

Expand the left side of the inequality

Using the Solving Inequalities knowledge point

$$ 2(x - 7) - 1 < -1x + 3 $$

$$ 2x - 14 - 1 < -x + 3 $$

Simplify the constant terms on the left side

Using the Solving Inequalities knowledge point

$$ 2x - 15 < -x + 3 $$

Add x to both sides of the inequality

Using the Solving Inequalities knowledge point

$$ 3x - 15 < 3 $$

Add 15 to both sides of the inequality

Using the Solving Inequalities knowledge point

$$ 3x < 18 $$

Divide both sides by 3 to solve for x

Using the Solving Inequalities knowledge point

$$ x < 6 $$

Answer:

The following inequality has a solution in the form \(x < A\). Solve the inequality and place the correct value of \(A\) into the box.

\(2(x - 7) - 1 < -1x + 3\)

Answer: \(x <\) <blank>6</blank>