The number we want to find is -10.4
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 {\boxed {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]\large {\boxed {y - y_1 = m ( x - x_1 )} }[/tex]
Let us tackle the problem.
Let :
The number = X
If ten times the sum of half a number and 6 is 8 , then :
[tex]10 \times ( \frac{1}{2} X + 6 ) = 8[/tex]
[tex]( 10 \times \frac{1}{2} X ) + ( 10 \times 6 ) = 8[/tex]
[tex]5 X + 60 = 8[/tex]
[tex]5 X = 8 - 60[/tex]
[tex]5 X = -52[/tex]
[tex]X = -52 \div 5[/tex]
[tex]\large {\boxed {X = -10.4} }[/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
