What is the minimum value of x for this inequality?
4x + 3( x - 1/5) ≥ 1/5( 2 + x )
How in the hell do I do this? Couldn't there be an infinite amount of numbers??
4x + 3( x - 1/5) ≥ 1/5( 2 + x )
Just simplify it
4x + 3x - 3/5 ≥ 2/5 + x/5
don't like those fractions? , multiply each term by 5
20x + 15x - 3 ≥ 2 + x
I am sure you can handle it from there, let me know what answer you get
I don't understand, what do you mean?
7x - 3/5 ≥ 2/5 + x/5
ok, let's go with your messy-looking equation
7x - 3/5 ≥ 2/5 + x/5
7x - x/5 ≥ 2/5 + 3/5
(35/5)x - (1/5)x ≥ 5/5
(34/5)x ≥ 1
now multiply each side by 5
34x ≥ 5
now divide each side by 34
x ≥ 5/34
starting from my simplified version of
20x + 15x - 3 ≥ 2 + x
20x + 15x - x ≥ 5
34x ≥ 5
x ≥ 5/34 , same result, less messy calculations
To find the minimum value of x for this inequality, we need to first simplify and solve for x. Here are the steps:
1. Expand both sides of the inequality:
4x + 3(x - 1/5) ≥ 1/5(2 + x)
4x + 3x - 3/5 ≥ 1/5 * (2 + x)
2. Combine like terms:
7x - 3/5 ≥ 2/5 + 1/5x
3. To get rid of the fractions, we can multiply both sides of the inequality by the least common denominator (LCD), which is 5:
5 * (7x - 3/5) ≥ 5 * (2/5 + 1/5x)
35x - 3 ≥ 2 + x
4. Simplify the equation:
35x - 3 ≥ 2 + x
5. Move all the x-terms to one side and the constant terms to the other side:
35x - x ≥ 2 + 3
34x ≥ 5
6. Divide both sides of the inequality by 34 to isolate x:
34x/34 ≥ 5/34
x ≥ 5/34
So, the minimum value of x that satisfies the inequality is x ≥ 5/34.
You are right that there could be an infinite number of numbers that satisfy the inequality. However, we can find the smallest possible value of x that makes the inequality true. In this case, that value is x ≥ 5/34.