Does π₯ = 1.6 satisfy the equation 6 β4π₯ = β x over 4?
Yes
6 - 4 x = - x / 4
Multiply both sides by 4
24 - 16 x = - x
Add 16 x to both sides
24 = 15 x
15 x = 24
Divide both sides by 15
x = 24 / 15 = 3 β 8 / 3 β 5 = 8 / 5 = 2 β 8 / 2 β 5 = 16 / 10 = 1.6
Check result:
6 - 4 x = - x / 4
6 - 4 β 1.6 = - 1.6 / 4
6 - 6.4 = - 0.4
- 0.4 = - 0.4
To determine if π₯ = 1.6 satisfies the equation, we can substitute the value of π₯ into the equation and check if both sides are equal.
Given equation: 6 - 4π₯ = -π₯/4
Substituting π₯ = 1.6 into the equation:
6 - 4(1.6) = -(1.6)/4
Simplifying the equation:
6 - 6.4 = -0.4
Since the left side of the equation is not equal to the right side, π₯ = 1.6 does not satisfy the equation 6 - 4π₯ = -π₯/4.
To determine if π₯ = 1.6 satisfies the equation 6 β4π₯ = βπ₯/4, we need to substitute π₯ = 1.6 into the equation and check if both sides are equal.
Step 1: Substitute π₯ = 1.6 into the equation.
6 - 4(1.6) = -1.6/4
Step 2: Simplify both sides of the equation.
6 - 6.4 = -0.4
Step 3: Evaluate the equation.
-0.4 = -0.4
Since both sides are equal (-0.4 = -0.4), π₯ = 1.6 satisfies the equation 6 - 4π₯ = -π₯/4.