Question

solve.
5x + 3 = - (x - 27)
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the solution is x = (type an integer or a fraction.)
b. the solution is all real numbers.
c. there is no solution.

Explanation:

Step1: Remove parentheses

Using the distributive property, $-(x - 27)$ becomes $-x + 27$. So the equation is $5x + 3 = -x + 27$.

Step2: Add x to both sides

Adding $x$ to each side: $5x + x + 3 = -x + x + 27$, which simplifies to $6x + 3 = 27$.

Step3: Subtract 3 from both sides

Subtract 3: $6x + 3 - 3 = 27 - 3$, so $6x = 24$.

Step4: Divide by 6

Divide both sides by 6: $\frac{6x}{6} = \frac{24}{6}$, giving $x = 4$.

Answer:

A. The solution is $x = 4$