Question

solve using the principles together. dont forget to check.
4 - 5a = a - 13

Explanation:

Step1: Isolate variable terms

Add $5a$ to both sides.
$4 - 5a + 5a = a - 13 + 5a$
$4 = 6a - 13$

Step2: Isolate constant terms

Add 13 to both sides.
$4 + 13 = 6a - 13 + 13$
$17 = 6a$

Step3: Solve for $a$

Divide both sides by 6.
$\frac{17}{6} = \frac{6a}{6}$
$a = \frac{17}{6}$

Step4: Verify the solution

Substitute $a=\frac{17}{6}$ into original equation.
Left side: $4 - 5\times\frac{17}{6} = 4 - \frac{85}{6} = \frac{24}{6} - \frac{85}{6} = -\frac{61}{6}$
Right side: $\frac{17}{6} - 13 = \frac{17}{6} - \frac{78}{6} = -\frac{61}{6}$
Both sides are equal, so the solution is valid.

Answer:

$a=\frac{17}{6}$