Question

solve the equation $-5 + \frac{1}{6}x + \frac{3}{4}x = -3$ for $x$. (hint: multiply both sides of the equation by the lcd and eliminate the fractions.)
enter each solution as an integer or reduced fraction only. decimal and mixed number answers will not be accepted.
$x = \boxed{}$

Explanation:

Step1: Find LCD of 6 and 4

The least common denominator of 6 and 4 is 12.

Step2: Multiply all terms by 12

$$12\times(-5) + 12\times\frac{1}{6}x + 12\times\frac{3}{4}x = 12\times(-3)$$
Simplify each term:
$$-60 + 2x + 9x = -36$$

Step3: Combine like terms

Combine the x-terms:
$$-60 + 11x = -36$$

Step4: Isolate the x-term

Add 60 to both sides:
$$11x = -36 + 60$$
$$11x = 24$$

Step5: Solve for x

Divide both sides by 11:
$$x = \frac{24}{11}$$

Answer:

$\frac{24}{11}$