Question

\\0.4x + 4.7(x + 2) + 2.6 < 47.7\\
\\0.4x + 4.7x + 9.4 + 2.6 < 47.7\\
\\5.1x + 12 < 47.7\\
\\5.1x < 35.7\\

Explanation:

Distribute and combine terms

Using the Multi-Step Inequalities knowledge point

$$
LATEXBLOCK0
$$

Isolate the variable term

Using the Solving Linear Inequalities knowledge point

$$
LATEXBLOCK1
$$

Solve for x

Using the Solving Linear Inequalities knowledge point

$$
LATEXBLOCK2
$$

Graph the solution

Using the Graphing Inequalities knowledge point

• An open circle is placed at \(x = 7\) because the inequality is strict (\(<\)).
• The arrow points to the left to represent all numbers less than 7.

Answer:

The solution to the inequality \(0.4x + 4.7(x + 2) + 2.6 < 47.7\) is <blank>\(x < 7\)</blank>.