Question

solve the equation: $\frac{1}{5}(x - 30) = 18 - 4x - 1$
step 1: simplify using the distributive property.
which number can be distributed across two terms inside parentheses?
step 2: combine like terms that are on the same side of the equation. which terms can be combined?
18 and -1
step 3: both sides of the equation contain a variable term.
you can isolate the variable term on either the left or right side of the equation. isolate the variable term by

Explanation:

Step1: Apply distributive property

$\frac{3}{5}(x - 10) = 18 - 4x - 1$
$\frac{3}{5}x - \frac{3}{5} \times 10 = 18 - 4x - 1$
$\frac{3}{5}x - 6 = 18 - 4x - 1$

Step2: Combine like terms (constants)

$\frac{3}{5}x - 6 = (18 - 1) - 4x$
$\frac{3}{5}x - 6 = 17 - 4x$

Step3: Isolate variable terms (add $4x$)

$\frac{3}{5}x + 4x - 6 = 17$
$\frac{3}{5}x + \frac{20}{5}x - 6 = 17$
$\frac{23}{5}x - 6 = 17$

Step4: Isolate variable (add 6)

$\frac{23}{5}x = 17 + 6$
$\frac{23}{5}x = 23$

Step5: Solve for $x$ (multiply by $\frac{5}{23}$)

$x = 23 \times \frac{5}{23}$
$x = 5$

Answer:

$x = 5$