Consider these equation and inequalities
2/3x=1/3x+1/4 2/3x <1\3x+1/4 2/3×>1\3x+1/4
Evaluate 2/3 x for x= 1/2
Evaluate 1/3x+1/4 for x= 1/2
Evaluate 2/3 x for x= 2
Evaluate 1/3x+1/4 for x=2
a. 2x/3 = (2*1/2)/3 = 1/3.
b. x/3 + 1/4 = (1/2)/3 + 1/4 = 1/2*1/3 + 1/4 = 1/6 + 1/4 = 2/12 + 3/12 = 5/12.
The student should do c, and d.
To evaluate the expressions with given values, we substitute the given values of x into the expressions and simplify.
1. Evaluate 2/3x for x= 1/2:
Substitute x = 1/2 into the expression 2/3x:
2/3 * (1/2)
To calculate this, we multiply the numerator of the fraction (2) by the numerator of the other fraction (1), and the denominator of the fraction (3) by the denominator of the other fraction (2):
(2 * 1) / (3 * 2)
Simplifying, we get:
2/6
Further simplifying by dividing both numerator and denominator by 2, we get:
1/3
So, when x=1/2, the value of 2/3x is 1/3.
2. Evaluate 1/3x + 1/4 for x= 1/2:
Substitute x = 1/2 into the expression 1/3x + 1/4:
1/3 * (1/2) + 1/4
To calculate this, we multiply the numerator of the fraction (1) by the numerator of the other fraction (1), and multiply the denominator of the fraction (3) by the denominator of the other fraction (2):
(1 * 1) / (3 * 2) + 1/4
= 1/6 + 1/4
To add these fractions, we need to find a common denominator which is 12:
(1/6 * 2/2) + (1/4 * 3/3)
= 2/12 + 3/12
Now, adding the fractions:
(2 + 3) / 12
= 5/12
So, when x=1/2, the value of 1/3x + 1/4 is 5/12.
3. Evaluate 2/3x for x= 2:
Substitute x = 2 into the expression 2/3x:
2/3 * 2
To calculate this, we multiply the numerator of the fraction (2) by the numerator of the other fraction (2):
(2 * 2) / 3
= 4/3
So, when x=2, the value of 2/3x is 4/3.
4. Evaluate 1/3x + 1/4 for x= 2:
Substitute x = 2 into the expression 1/3x + 1/4:
1/3 * 2 + 1/4
To calculate this, we multiply the numerator of the fraction (1) by the numerator of the other fraction (2):
(1 * 2) / 3 + 1/4
= 2/3 + 1/4
To add these fractions, we need to find a common denominator which is 12:
(2/3 * 4/4) + (1/4 * 3/3)
= 8/12 + 3/12
Now, adding the fractions:
(8 + 3) / 12
= 11/12
So, when x=2, the value of 1/3x + 1/4 is 11/12.