Question

solve.
$\frac{x+7}{3}+\frac{x-1}{2}=\frac{8}{3}$

Explanation:

Step1: Find common denominator

The common denominator of 3, 2, 3 is 6. Multiply each term by 6 to eliminate fractions:
$$6\times\frac{x+7}{3} + 6\times\frac{x-1}{2} = 6\times\frac{8}{3}$$

Step2: Simplify each term

Calculate the product for each term:
$$2(x+7) + 3(x-1) = 16$$

Step3: Expand parentheses

Distribute the coefficients to the terms inside parentheses:
$$2x + 14 + 3x - 3 = 16$$

Step4: Combine like terms

Combine the variable terms and constant terms:
$$5x + 11 = 16$$

Step5: Isolate the variable term

Subtract 11 from both sides of the equation:
$$5x = 16 - 11$$
$$5x = 5$$

Step6: Solve for x

Divide both sides by 5:
$$x = \frac{5}{5}$$

Answer:

$x=1$