Question

Find the solution set of the inequality \qquad4x -1 < 11.4x−1<11.4, x, minus, 1, is less than, 11, point \qquad xxx

Answer 1

Answer:

(∞, 3]

Step-by-step explanation:

Given the inequality 4x−1<11

We are to find the solution set;

4x−1<11

Add 1 to both sides

4x−1+1<11+1

4x < 12

Divide both sides by 4

4x/4 = 12/4

x < 3

Hence the solution set of the inequality is (∞, 3]

Answer 2

Answer:

x > 5.

Step-by-step explanation:

1 / 3

Let’s start by subtracting \blue{14}14start color #6495ed, 14, end color #6495ed from both sides of the inequality:

\qquad\begin{aligned} 14\blue{-14} - 3x &< -1 \blue{-14}\\ - 3x &< -15 \\ \end{aligned}  

14−14−3x

−3x

​  

 

<−1−14

<−15

​  

 

Hint #22 / 3

Next, let's divide both sides by \green{-3}−3start color #28ae7b, minus, 3, end color #28ae7b. When you divide an inequality by a negative number, the inequality sign must be \text{\pink{reversed}}reversedstart text, start color #ff00af, r, e, v, e, r, s, e, d, end color #ff00af, end text:

\qquad\begin{aligned} - 3x& < -15\\ \\ \dfrac{-3x}{\green{-3}} &\pink{>} \dfrac{-15}{\green{-3}} \\ \\ x &\pink{>} 5\\ \end{aligned}  

−3x

−3

−3x

​  

 

x

​  

 

<−15

>  

−3

−15

​  

 

>5

​  

 

Hint #33 / 3

The solution set of the inequality is:

\qquad x > 5.

x>5.