Question

Which represents the solution set to the inequality 5.1(3 + 2.2x) > –14.25 – 6(1.7x + 4)?

Answer 1

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 :

$\large {m = \frac{y_2 - y_1}{x_2 - x_1}$

If point ( x₁ , y₁ ) is on the line with gradient m , the equation of the line will be :

$y - y_1 = m ( x - x_1 )$

Let us tackle the problem.

Given:

$5.1(3 + 2.2x) > -14.25 - 6(1.7x + 4)$

$(5.1 \times 3) + (5.1 \times 2.2x) > -14.25 - (6 \times 1.7x + 6 \times 4)$ → distributive law of multiplication

$(15.3) + (11.22x) > -14.25 - (10.2x + 24)$

$15.3 + 11.22x > -14.25 - 10.2x - 24$

$11.22x + 10.2x > -14.25 - 15.3 - 24$ → rearrange

$21.42x > -53.55$

$x > -53.55 \div 21.42$

$x > -5/2$

$\large {\boxed {x > -2.5} }$

Learn more

• Infinite Number of Solutions : brainly.com/question/5450548
• System of Equations : brainly.com/question/1995493
• System of Linear equations : brainly.com/question/3291576

Answer details

Grade: High School

Subject: Mathematics

Chapter: Linear Equations

Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point

Answer 2

1. Simplify the inequality $5.1(3 + 2.2x) > -14.25 - 6(1.7x + 4):$

$15.3+11.22x>-14.25-10.2x-24,\\ 15.3+11.22x>-10.2x-38.75.$

2. Separate terms with x and without x in different sides:

$11.22x+10.2x>-38.75-15.3.$

3. Add similar terms:

$21.42x>-54.05.$

4. Divide by 21.42:

$x>-\dfrac{54.05}{21.42} ,\\ \\x>-2.5.$

Answer: correct choice is C.