Question

solve for x.

1 = \frac{7x - 3}{5} - \frac{5x + 4}{6}

simplify your answer as much as possible.

x = \square

Explanation:

Step1: Find common denominator

The denominators are 5 and 6, so the common denominator is 30. Multiply each term by 30 to eliminate fractions:
$$30\times1 = 30\times\frac{7x - 3}{5}-30\times\frac{5x + 4}{6}$$
Simplify each term:
$$30 = 6(7x - 3)-5(5x + 4)$$

Step2: Distribute the terms

Distribute 6 and 5 in the parentheses:
$$30 = 42x - 18 - 25x - 20$$

Step3: Combine like terms

Combine the x - terms and the constant terms:
$$30 = (42x - 25x)+(-18 - 20)$$
$$30 = 17x - 38$$

Step4: Solve for x

Add 38 to both sides:
$$30 + 38 = 17x$$
$$68 = 17x$$
Divide both sides by 17:
$$x=\frac{68}{17}=4$$

Answer:

\( x = 4 \)