Certainly! Let's solve the given inequality step-by-step:
### Step-by-Step Solution
1. Given Inequality:
[tex]\[
10 + 4x < 14
\][/tex]
2. Isolate the Term with [tex]\( x \)[/tex]:
Subtract 10 from both sides to start isolating the term with [tex]\( x \)[/tex]:
[tex]\[
10 + 4x - 10 < 14 - 10
\][/tex]
Simplifying both sides of the inequality we have:
[tex]\[
4x < 4
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
Divide both sides of the inequality by 4 to solve for [tex]\( x \)[/tex]:
[tex]\[
\frac{4x}{4} < \frac{4}{4}
\][/tex]
Simplifying the inequality we get:
[tex]\[
x < 1
\][/tex]
The solution to the inequality [tex]\( 10 + 4x < 14 \)[/tex] is:
[tex]\[
x < 1
\][/tex]
### Plotting the Solution on Number Line
To represent [tex]\( x < 1 \)[/tex] on a number line, we mark everything to the left of 1, not including 1 itself (since [tex]\( x \)[/tex] is strictly less than 1). We can indicate this using an open circle at 1 and shading to the left:
[tex]\[
\begin{array}{ccccccc}
\longrightarrow & 0 & \longrightarrow & 1 & \longrightarrow & 4 & \\
& O & \longrightarrow & \circ & \longleftarrow & \\
\end{array}
\][/tex]
The open circle at 1 ( [tex]\( \circ \)[/tex] ) shows that 1 is not included in the solution, and the shading to the left indicates all values less than 1 are part of the solution set.
Therefore, the solution set is:
[tex]\[
\boxed{x < 1}
\][/tex]
And the number line representation correctly shows this range.
