Solve the following equations for the variable:

Question

ScanSolve AI Tutor · Accepted Answer

Here are the solutions to the equations:

1. $3a = 10 + 9$

Simplify the right side of the equation.
$3a = 19$
Divide both sides by 3 to solve for $a$ .
$a = \frac{19}{3}$ $\boxed{a = \frac{19}{3}}$
2. $12 - 3m = 2m - 3$
Add $3m$ to both sides of the equation.
$12 = 2m + 3m - 3$ $12 = 5m - 3$
Add 3 to both sides of the equation.
$12 + 3 = 5m$ $15 = 5m$
Divide both sides by 5 to solve for $m$ .
$\frac{15}{5} = m$ $3 = m$ $\boxed{m = 3}$
3. $3 + \frac{1}{2}x = 2\frac{1}{4}x - 1$
Convert the mixed number to an improper fraction.
$2\frac{1}{4} = \frac{2 \times 4 + 1}{4} = \frac{9}{4}$
The equation becomes:
$3 + \frac{1}{2}x = \frac{9}{4}x - 1$
Subtract $\frac{1}{2}x$ from both sides of the equation.
$3 = \frac{9}{4}x - \frac{1}{2}x - 1$ $3 = \frac{9}{4}x - \frac{2}{4}x - 1$ $3 = \frac{7}{4}x - 1$
Add 1 to both sides of the equation.
$3 + 1 = \frac{7}{4}x$ $4 = \frac{7}{4}x$
Multiply both sides by $\frac{4}{7}$ to solve for $x$ .
$4 \times \frac{4}{7} = x$ $\frac{16}{7} = x$ $\boxed{x = \frac{16}{7}}$

Answer