Question

1. solve for x. no decimals.

a. \\(\frac{4x}{3} - \frac{5}{2} = \frac{7x}{4}\\)

Explanation:

Step1: Find common denominator

The least common denominator of 3, 2, and 4 is 12. Multiply each term by 12 to eliminate fractions.
$$12\times\frac{4x}{3} - 12\times\frac{5}{2} = 12\times\frac{7x}{4}$$

Step2: Simplify each term

Calculate the product for each term.
$$16x - 30 = 21x$$

Step3: Isolate x terms

Subtract $16x$ from both sides to group x terms on one side.
$$-30 = 21x - 16x$$

Step4: Combine like terms

Simplify the right-hand side of the equation.
$$-30 = 5x$$

Step5: Solve for x

Divide both sides by 5 to solve for x.
$$x = \frac{-30}{5}$$

Answer:

$x = -6$