Question

mpm2d
name:

1. algebraically, solve the following equation then perform left side/right side check.

solve
check
$\frac{x+3}{6} = \frac{2x-1}{9}$
$\frac{x+3}{6} \times 6 = \frac{2x-1}{9} \times 9$
$6x+18 = 18x - 9$
$6x - 18x = -9-18$
$-12x = 27$
ls =
rs =

Explanation:

Step1: Correct cross-multiplication

The original equation is $\frac{x+3}{6} = \frac{2x-1}{9}$. Cross-multiply to eliminate denominators:
$9(x+3) = 6(2x-1)$

Step2: Expand both sides

Distribute the coefficients:
$9x + 27 = 12x - 6$

Step3: Isolate x terms

Subtract $9x$ from both sides:
$27 = 3x - 6$

Step4: Isolate constant terms

Add 6 to both sides:
$33 = 3x$

Step5: Solve for x

Divide both sides by 3:
$x = \frac{33}{3} = 11$

Step6: Left Side (LS) check

Substitute $x=11$ into $\frac{x+3}{6}$:
$\frac{11+3}{6} = \frac{14}{6} = \frac{7}{3}$

Step7: Right Side (RS) check

Substitute $x=11$ into $\frac{2x-1}{9}$:
$\frac{2(11)-1}{9} = \frac{22-1}{9} = \frac{21}{9} = \frac{7}{3}$

Answer:

The solution is $x=11$.
Check:
LS = $\frac{7}{3}$, RS = $\frac{7}{3}$, so LS=RS, confirming the solution is correct.