Final answer:
The value of x that satisfies the equation -4x (-3/5x) = -3(2x/8) are x = 0 and x = -5/16. This result is obtained by simplifying both sides, factoring out common terms, and solving the resulting simple equations.
Step-by-step explanation:
The student's question is asking what value of x will satisfy the equation -4x (-3/5x) = -3(2x/8). To solve the equation, we need to apply the properties of multiplication and division of real numbers and solve for x.
First, let's simplify both sides of the equation:
-4x (-3/5x) simplifies to 12/5x², because when two negative numbers multiply, the result is positive as per the known multiplication rules.
On the right side, -3(2x/8) simplifies to -3x/4, since we have -3 multiplied by 1/4 of 2x.
Now we have:
12/5x² = -3x/4
To solve for x, we multiply both sides by the Least Common Denominator (LCD) which is 20 in this case, to eliminate the fractions:
20 * (12/5x²) = 20 * (-3x/4)
This gives us:
48x² = -15x
Next, we set the equation equal to zero and factor out the common term, which is x:
x(48x + 15) = 0
We now have two possible solutions:
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- x = 0
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- 48x + 15 = 0 which gives x = -15/48 or x = -5/16 after simplification
Therefore, the values of x that make the equation true are x = 0 and x = -5/16.