Question

solve the equation and check.
\\(\frac{11t}{28} - \frac{t}{4} = 1\\)

select the correct choice below and, if necessary, fill in the answer box to complete your choice
\\(\bigcirc\\) a. \\(t = \square\\) (simplify your answer.)
\\(\bigcirc\\) b. the solution is all real numbers.
\\(\bigcirc\\) c. there is no solution.

Explanation:

Step1: Make denominators equal

Rewrite $\frac{t}{4}$ as $\frac{7t}{28}$, so the equation becomes:
$$\frac{11t}{28} - \frac{7t}{28} = 1$$

Step2: Combine like terms

Subtract the fractions:
$$\frac{11t - 7t}{28} = 1$$
$$\frac{4t}{28} = 1$$
Simplify the fraction:
$$\frac{t}{7} = 1$$

Step3: Solve for t

Multiply both sides by 7:
$$t = 7 \times 1$$

Step4: Check the solution

Substitute $t=7$ into the original equation:
$$\frac{11 \times 7}{28} - \frac{7}{4} = \frac{77}{28} - \frac{49}{28} = \frac{28}{28} = 1$$
The left side equals the right side, so the solution is valid.

Answer:

A. t=7 (Simplify your answer)