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Solve each linear equation. See Examples 1–3. -4 (2x - 6) + 8x = 5x + 24 + x
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0. Review of College Algebra
Solving Linear Equations
Scelta multipla
Solve the equation. Then state whether it is an identity, conditional, or inconsistent equation.
A
Identity
B
Conditional
C
Inconsistent
Guida verificata passo dopo passo1
Start by simplifying the given equation: \( \frac{x}{4} + \frac{1}{6} = \frac{x}{3} \). To eliminate the fractions, find a common denominator, which is 12.
Multiply each term by 12 to clear the fractions: \( 12 \times \frac{x}{4} + 12 \times \frac{1}{6} = 12 \times \frac{x}{3} \). This simplifies to \( 3x + 2 = 4x \).
Rearrange the equation to isolate terms involving x on one side: Subtract 3x from both sides to get \( 2 = x \).
Now that you have solved for x, check if the solution satisfies the original equation. Substitute x = 2 back into the original equation to verify.
Determine the type of equation: Since there is a specific solution (x = 2), the equation is conditional. An identity would be true for all values of x, and an inconsistent equation would have no solution.
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