The value of x is 25.
What are some of the properties of real numbers?
For real numbers, a, b, and c with operations addition and multiplication following are some of the properties
- a + 0 = a
- a + (-a) = 0
- 1 × a = a
- a × (1/a) = 1, a ≠ 0
- -a = (-1) × a
- (a × b) × c = a × (b × c)
Given
LM = MN,
LM = 43,
MN = 2x - 7.
Obtain the equation for x
LM = MN. ...(1)
We are given LM = 43. So, if we substitute LM for 43 in equation (1), it follows that MN = 43.
But MN = 2x - 7, so again using the transitive property of the equality, we obtain
2x - 7 = 43, ...(2)
which is the equation in x to be solved to obtain the value of x.
Solve for x
Calculate 2x - 7 + 7. In this expression, we can substitute the value of 2x - 7 from equation (2). By substituting we get the equation
2x - 7 + 7 = 43 + 7.
Since we know a - b = a + (-b) - i.e., subtracting b from a is the same as adding the additive inverse of b to a - we can write the above equation as
2x + (-7) + 7 = 50.
Adding to a number its additive inverse yields the identity element 0. So, 2x + 0 = 50.
Adding the identity element to a number does nothing to it. So, 2x = 50.
Multiply the multiplicative inverse of 2 on both sides we get,
(1/2) × (2x) = (1/2) × 50.
Multiplication is associative. So, we can write ((1/2) × 2) × x = 25.
Multiplying to a number its multiplicative inverse gives the identity element under multiplication i.e. 1. So, 1 × x = 25.
Multiplying 1 to a number does nothing to it. So we get, x = 25.
The required value of x is 25.
Learn more about the properties of real numbers here
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