Enter the value of x that makes the given equation true 12x = 3
2 answers:
The value of x that makes the given equation true :
An equation means what is on the left is equal to what is on the right
The equation will be true if we put a value into the variable that makes the equation true.
One variable linear equation is an equation that has a variable and the exponent number is one.
Can be stated in the form:
or
ax + b = c,
where a, b, and c are constants, x is a variable
There are several ways to solve an equation
- Add / Subtract / divide / multiply the same value on both sides
- Combine like terms
- Factoring
- Expanding
In the equation
12x = 3
we can solve with 2 ways :
- 1. dividing
we divide both sides by 12 to get the value x
12x: 12 = 3:12
- 2. factoring
we move number 3 to the left
12x-3 = 0
factoring :
3 (4x-1) = 0
3≠ 0 ---> no solution
4x-1 = 0
- add 1 to both sides
4x-1 + 1 = 0 + 1
4x = 1
- divide 4
4x: 4 = 1: 4
the slope-intercept form of the linear equation
a graph of a linear equation
system of linear equations
Keywords : one variable, linear equation ,the value of x, solution, true
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Refer to the figure shown below.
x = the width of the rectangle (meters)
y = the height of the rectangle (meters(
The fencing for the perimeter of the rectangle costs $30 per meter.
The two inner partitions cost $25 per meter.
The total cost of the fencing is
C = 2(x+y)*$30 + 2y*$25
= 60(x+y) + 50y
= 60x + 110y
Because the amount available to spend is $600, therefore
60x + 110y = 6000
or
6x + 11y = 600
That is,
y = (600 - 6x)/11 (1)
The area is
A = x*y (2)
Substitute (1) into (2).
A = (x/11)*(600 - 6x) = (1/11)*(600x - 6x²)
To maximize A, the derivative of A with respect to x is zero.
That is,
600 - 12x = 0
x = 600/12 = 50
From (1), obtain
y = (1/11)*(600 - 6*50) = 300/11 = 27.273
Because the second derivative of A with respect to x is negative, x=50, y = 27.273 will yield the maximum area.
The maximum area is
50*27.273 = 1363.64 m² = 1364 m² (nearest integer)
Answer: 1364 m² (nearest integer)
x = the width of the rectangle (meters)
y = the height of the rectangle (meters(
The fencing for the perimeter of the rectangle costs $30 per meter.
The two inner partitions cost $25 per meter.
The total cost of the fencing is
C = 2(x+y)*$30 + 2y*$25
= 60(x+y) + 50y
= 60x + 110y
Because the amount available to spend is $600, therefore
60x + 110y = 6000
or
6x + 11y = 600
That is,
y = (600 - 6x)/11 (1)
The area is
A = x*y (2)
Substitute (1) into (2).
A = (x/11)*(600 - 6x) = (1/11)*(600x - 6x²)
To maximize A, the derivative of A with respect to x is zero.
That is,
600 - 12x = 0
x = 600/12 = 50
From (1), obtain
y = (1/11)*(600 - 6*50) = 300/11 = 27.273
Because the second derivative of A with respect to x is negative, x=50, y = 27.273 will yield the maximum area.
The maximum area is
50*27.273 = 1363.64 m² = 1364 m² (nearest integer)
Answer: 1364 m² (nearest integer)