%2F4-%3D-(x%2B7)%2F3.jpeg "(2x+3)/4 = (x+7)/3")
Solving the Equation: (2x+3)/4 = (x+7)/3
This article will guide you through the process of solving the equation (2x+3)/4 = (x+7)/3.
Understanding the Equation
The equation (2x+3)/4 = (x+7)/3 represents a fractional equation. This means that the unknown variable (x) is part of a fraction. To solve for x, we need to get rid of the fractions and isolate x on one side of the equation.
Solving for x
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Cross-Multiplication: Begin by cross-multiplying the fractions. This involves multiplying the numerator of the first fraction by the denominator of the second fraction, and vice versa. This gives us: 3(2x+3) = 4(x+7)
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Expand: Expand both sides of the equation by distributing the numbers: 6x + 9 = 4x + 28
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Combine Like Terms: Move all the x terms to one side of the equation and the constant terms to the other side. Subtract 4x from both sides and subtract 9 from both sides: 6x - 4x = 28 - 9
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Simplify: Simplify both sides of the equation: 2x = 19
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Isolate x: Divide both sides by 2 to isolate x: x = 19/2
Solution
Therefore, the solution to the equation (2x+3)/4 = (x+7)/3 is x = 19/2.
Verification
To verify our solution, we can substitute x = 19/2 back into the original equation:
(2*(19/2)+3)/4 = (19/2 + 7)/3
Simplifying both sides, we get:
(19+3)/4 = (19/2 + 14/2)/3
22/4 = 33/6
11/2 = 11/2
Since both sides of the equation are equal, we have verified that our solution x = 19/2 is correct.