The solution set to the inequality is C) (–2.5, ∞)
Further explanation
Solving linear equation mean calculating the unknown variable from the equation.
Let the linear equation : y = mx + c
If we draw the above equation on Cartesian Coordinates , it will be a straight line with :
m → gradient of the line
( 0 , c ) → y - intercept
Gradient of the line could also be calculated from two arbitrary points on line ( x₁ , y₁ ) and ( x₂ , y₂ ) with the formula :
[tex]\large {m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
If point ( x₁ , y₁ ) is on the line with gradient m , the equation of the line will be :
[tex]y - y_1 = m ( x - x_1 )[/tex]
Let us tackle the problem.
Given:
[tex]5.1(3 + 2.2x) > -14.25 - 6(1.7x + 4)[/tex]
[tex](5.1 \times 3) + (5.1 \times 2.2x) > -14.25 - (6 \times 1.7x + 6 \times 4)[/tex] → distributive law of multiplication
[tex](15.3) + (11.22x) > -14.25 - (10.2x + 24)[/tex]
[tex]15.3 + 11.22x > -14.25 - 10.2x - 24[/tex]
[tex]11.22x + 10.2x > -14.25 - 15.3 - 24[/tex] → rearrange
[tex]21.42x > -53.55[/tex]
[tex]x > -53.55 \div 21.42[/tex]
[tex]x > -5/2[/tex]
[tex]\large {\boxed {x > -2.5} }[/tex]
Learn more
- Infinite Number of Solutions : https://brainly.com/question/5450548
- System of Equations : https://brainly.com/question/1995493
- System of Linear equations : https://brainly.com/question/3291576
Answer details
Grade: High School
Subject: Mathematics
Chapter: Linear Equations
Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point
